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ODSC East 2017 Probabilistic Programming in Python with PyMC3
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"The code in the following cell converts this notebook to an HTML slideshow powered by [reveal.js](http://lab.hakim.se/reveal-js/)."
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"[NbConvertApp] Converting notebook ./ODSC East 2017 Probabilistic Programming in Python with PyMC3.ipynb to slides\n",
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"source": [
"%%bash\n",
"jupyter nbconvert \\\n",
" --to=slides \\\n",
" --reveal-prefix=https://cdnjs.cloudflare.com/ajax/libs/reveal.js/3.2.0/ \\\n",
" --output=pp-pymc3-odsc-east-2017 \\\n",
" ./ODSC\\ East\\ 2017\\ Probabilistic\\ Programming\\ in\\ Python\\ with\\ PyMC3.ipynb"
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"source": [
"A Dockerfile that will produce a container with all the dependencies necessary to run this notebook is available [here](https://github.com/AustinRochford/notebooks)."
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"%matplotlib inline"
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"source": [
"from contextlib import contextmanager\n",
"import datetime\n",
"import logging\n",
"from warnings import filterwarnings\n",
"\n",
"from IPython.display import HTML"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true,
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"source": [
"from matplotlib import pyplot as plt\n",
"from matplotlib.animation import ArtistAnimation\n",
"from matplotlib.patches import Ellipse\n",
"from matplotlib.ticker import FuncFormatter\n",
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import theano"
]
},
{
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"execution_count": 4,
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"source": [
"# make theano go a bit faster\n",
"theano.config.floatX = 'float32'"
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"# configure pyplot for readability when rendered as a slideshow and projected\n",
"plt.rc('figure', figsize=(8, 6))\n",
"\n",
"LABELSIZE = 14\n",
"plt.rc('axes', labelsize=LABELSIZE)\n",
"plt.rc('axes', titlesize=LABELSIZE)\n",
"plt.rc('figure', titlesize=LABELSIZE)\n",
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"\n",
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"blue, green, red, purple, gold, teal = sns.color_palette()\n",
"\n",
"pct_formatter = FuncFormatter(lambda p, _: '{:.1%}'.format(p))"
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"source": [
"filterwarnings('ignore', 'findfont')"
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"source": [
"SEED = 72966 # from random.org, for reproducibility\n",
"\n",
"np.random.seed(SEED)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Probabilistic Programming in Python with PyMC3\n",
"\n",
"<center><img src='https://raw.githubusercontent.com/pymc-devs/pymc3/master/docs/pymc3_logo.jpg'></center>\n",
"\n",
"\n",
"## #ODSC East, Boston &#8226; May 5, 2017 &#8226; [@AustinRochford](https://twitter.com/AustinRochford)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
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},
"source": [
"## About Me\n",
"\n",
"<center><img src='http://austinrochford.com/resources/img/face_big.png' width=400></center>\n",
"\n",
"### [@AustinRochford](https://twitter.com/AustinRochford) &#8226; [austinrochford.com](http://austinrochford.com) &#8226; [github.com/AustinRochford](http://github.com/AustinRochford)\n",
"\n",
"### [austin.rochford@gmail.com](mailto:arochford@monetate.com) &#8226; [arochford@monetate.com](mailto:arochford@monetate.com)\n",
"\n",
"### PyMC3 contributor &#8226; Principal Data Scientist at [Monetate Labs](http://www.monetate.com/)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Probabilistic Programming\n",
"\n",
"* Write a program to simulate the data generating process\n",
"* Language runtime/software library performs inference"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<center><img src=\"http://austinrochford.com/resources/talks/img/probabilistic_programming.png\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Data Science &mdash; inference enables storytelling\n",
"\n",
"<center><a href=\"https://en.wikipedia.org/wiki/Charles_Joseph_Minard#Work\"><img src=\"https://www.edwardtufte.com/tufte/graphics/minard_lg.gif\" width=\"800\"></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Probabilistic Programming &mdash; storytelling enables inference\n",
"\n",
"<img src=\"http://austinrochford.com/resources/talks/img/prob_prog_png.png\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"#### Enter: Bayes theorem\n",
"\n",
"<center><img src=\"https://upload.wikimedia.org/wikipedia/commons/1/18/Bayes'_Theorem_MMB_01.jpg\" width=600>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"#### Benefits of probabilistic programming\n",
"\n",
"* Model-agnostic inference algorithms\n",
"* Quantification of uncertainty\n",
"* _Incorporation of domain knowledge_\n",
"* _Modularity_"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"#### The Monty Hall Problem\n",
"\n",
"<br>\n",
"\n",
"<center><img src='https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Monty_open_door.svg/640px-Monty_open_door.svg.png'></center>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"The [Monty Hall problem](https://en.wikipedia.org/wiki/Monty_Hall_problem) is named after the host of the 1960s television show [_Lets Make a Deal_](https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal)."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
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},
"source": [
"Initially, we have no information about which door the prize is behind."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"import pymc3 as pm\n",
"\n",
"with pm.Model() as monty_model:\n",
" prize = pm.DiscreteUniform('prize', 0, 2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"If we choose door one:\n",
"\n",
"<table>\n",
" <tr>\n",
" <td></td>\n",
" <th colspan=\"3\"><center>Monty can open</center></th>\n",
" </tr>\n",
" <tr>\n",
" <th>Prize behind</th>\n",
" <td>Door 1</td>\n",
" <td>Door 2</td>\n",
" <td>Door 3</td>\n",
" </tr>\n",
" <tr>\n",
" <td>Door 1</td>\n",
" <td><font color=\"red\">No</font></td>\n",
" <td><font color=\"green\">Yes</font></td>\n",
" <td><font color=\"green\">Yes</font></td>\n",
" </tr>\n",
" <tr>\n",
" <td>Door 2</td>\n",
" <td><font color=\"red\">No</font></td>\n",
" <td><font color=\"red\">No</font></td>\n",
" <td><font color=\"green\">Yes</font></td>\n",
" </tr>\n",
" <tr>\n",
" <td>Door 2</td>\n",
" <td><font color=\"red\">No</font></td>\n",
" <td><font color=\"green\">Yes</font></td>\n",
" <td><font color=\"red\">No</font></td>\n",
" </tr>\n",
"</table>"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"from theano import tensor as tt\n",
"\n",
"with monty_model:\n",
" p_open = pm.Deterministic('p_open',\n",
" tt.switch(tt.eq(prize, 0),\n",
" # it is behind the first door\n",
" np.array([0., 0.5, 0.5]),\n",
" tt.switch(tt.eq(prize, 1),\n",
" # it is behind the second door\n",
" np.array([0., 0., 1.]),\n",
" # it is behind the third door\n",
" np.array([0., 1., 0.]))))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Monty opened the third door, revealing a goat.\n",
"\n",
"<center><img src='https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Monty_open_door.svg/640px-Monty_open_door.svg.png' width='500'></center>"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"with monty_model:\n",
" opened = pm.Categorical('opened', p_open, observed=2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Should we switch our choice of door?"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Assigned Metropolis to prize\n",
"100%|██████████| 1000/1000 [00:00<00:00, 2850.75it/s]\n"
]
}
],
"source": [
"with monty_model:\n",
" monty_trace = pm.sample(1000, init=None, random_seed=SEED)\n",
" \n",
"monty_df = pm.trace_to_dataframe(monty_trace)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
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" <th>prize</th>\n",
" <th>p_open__0</th>\n",
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" prize p_open__0 p_open__1 p_open__2\n",
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"monty_df.prize.mean()"
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0uE9RUZGSk5OVkJCgnJwceXt7y2Kx6P7775e3t7f27dt3i7MCAKBh+VVB4uzZs9q3b5+u\nXLlyywcuLi5Wbm6uPD091bZtW3l6eiozM9Nue1ZWlgIDAyscIyAgwK6PJGVmZlbYZ9asWRoyZIja\ntm0rwzB09epV27aSkhKVlZXd4qwAAGhYHLq0ceHCBU2ePFkZGRlycnLStm3b5OXlpalTp8rT01Mv\nv/zyTceYPXu2HnnkEbVu3Vpnz57VO++8o0uXLqlfv35ycnJSdHS0Fi1apA4dOqhdu3ZauHCh3Nzc\n9Pjjj9vGGDp0qPz8/DR+/HhJUnR0tAYPHqzFixcrLCxMO3bs0K5du7Rq1apyx8/MzNSRI0c0Y8YM\nSZKvr69yc3O1c+dOlZWVKTc3V76+vg59aQAA4BqHgsSbb76pU6dOadOmTXr22Wdt7Y888oiSkpIc\nChL//Oc/NW7cOP34449q3ry5AgICtG7dOt17772SpBEjRqi4uFiJiYk6d+6c/P39lZqaavcMiRMn\nTqh169a2z0FBQZo3b57mz5+vlJQUeXl5KSkpybbm4rrLly8rISFBSUlJtmdXtGrVSgkJCZo2bZoM\nw1BiYqJatWrlyNcBAAD+PyfDMIyb7fTQQw/prbfekp+fnwIDA7V582Z5eXnp+PHjevLJJ5WdnV0d\ntdYK9X1lbn3HXRuorYbN2lnTJeAWpE7qXdMlVKnK7tpwaI3ETz/9pObNm5drv3jxot3TKQEAQMPi\nUJDw9fXVf/3Xf5VrX7NmTaWLIQEAQP3m0BqJuLg4DR8+XEeOHFFpaanef/99HT58WF999ZVWrFhR\n1TUCAIBayqEzEkFBQVqzZo1KSkp033336fPPP1fLli21Zs0aderUqaprBAAAtZTDT7a0Wq2aPXt2\nVdYCAADqGIfOSERHR+vtt98u137u3DlFR0ff9qIAAEDd4NAZid27d+vgwYM6dOiQ5syZI1dXV0nX\nnga5Z8+eKi0QAADUXg4/Ivu9995Tfn6+nn322UrfyAkAABoOh4PEPffco9WrV+u+++7T008/ra+/\n/roq6wIAAHWAQ0Hi+mu5/+3f/k3z58/XH/7wBw0ZMkR/+9vfqrQ4AABQuzm0RuJfn6I9evRodezY\nUa+++mqVFAUAAOoGh4LE8uXLddddd9m19e3bVx06dNA333xTJYUBAIDaz6Eg0a1btxu2+/j4yMfH\n57YWBAAA6o4Kg8SoUaP05ptvqmnTpho1alSlgyxatOi2FwYAAGq/CoPEL9/2effdd9sWXAIAAFxX\nYZCYOXOm7e/Tpk1T48aNeWU4AACwc9PbP0tLS/XAAw8oNze3OuoBAAB1yE2DhLOzs9q0aaOSkpLq\nqAcAANQhDj2Q6o9//KPefPNNnT17tqrrAQAAdYhDt3+mpqYqPz9fDz30kO655x41adLEbvuWLVuq\npDgAAFC7ORQkwsPDq7oOAABQBzkUJEaPHl3VdQAAgDrIoSBx3eeff66jR49KkiwWi4KDg6ukKAAA\nUDc4FCROnDihl19+Wd9++61atmwpSTp9+rR8fHyUkpIiLy+vKi0SAADUTg7dtTF58mQ1bdpUO3bs\n0CeffKJPPvlEO3bsULNmzTR58uSqrhEAANRSDgWJnJwcTZkyRW3atLG1tWnTRv/5n/+pnJycKisO\nAADUbg4FidatW+vy5cvl2ouLi9W6devbXhQAAKgbHAoSkyZN0vTp05WTk6PS0lKVlpYqJydHM2bM\n0MSJE6u6RgAAUEs5tNhy3LhxKikpUVRUlH7zm2vZo6ysTM7OzpowYYLdvl9++eXtrxIAANRKDgWJ\nqVOnVnUdAACgDnIoSPTr16+q6wAAAHWQQ2skAAAAboQgAQAATCNIAAAA0yoMEidPnpRhGNVZCwAA\nqGMqDBKPPvqozp49K0mKjo7WTz/9dFsPvGjRIlmtViUmJtraDMNQSkqKQkND5efnpyFDhujw4cM3\nHSsjI0MRERHq3LmzIiIitH37drvty5YtU0hIiIKDg5Wammq3bf/+/QoPD7/hA7cAAEDlKgwSd9xx\nh4qKiiRJu3fv1tWrV2/bQXNycrRu3TpZrVa79qVLlyo1NVXx8fHasGGDWrRooZiYGF24cKHCsbKz\nsxUXF6fIyEilp6crMjJSY8aM0b59+yRJBw8e1IIFCzR37lzNmzdP8+fP16FDhyRJpaWlmjJliqZN\nmyZXV9fbNj8AABqKCm//DAkJ0dChQ9WhQwdJ0ksvvaRGjRrdcN/ly5c7fMDz589rwoQJev311/XO\nO+/Y2g3D0PLlyzVy5EiFh4dLkmbPnq3g4GBt3bpVgwYNuuF4aWlp6t69u2JjYyVJsbGx2rVrl9LS\n0jRv3jwdO3ZMVqvV9spzq9Vqa0tLS5OPj49CQkIcrh8AAPyfCoPEnDlztHHjRn333Xfas2eP2rdv\nryZNmtzyAePj4xUeHq7g4GC7IJGfn6+CggL16NHD1ubq6qquXbsqOzu7wiCRk5OjwYMH27WFhoZq\n5cqVkq4Fh7y8PNuaj7y8PPn4+Cg/P18rVqzQxo0bf1X9zZu7ycXF+Vf1Qe3i6dmspksAUM805H9X\nKgwSrq6ueu655yRJBw4c0KRJk3TnnXfe0sHWrVun48ePa86cOeW2FRQUSJI8PDzs2t3d3XX69OkK\nxywsLCzXx8PDwzaexWJRXFycYmJiJF173LfFYtHw4cMVFxenvXv3Kjk5WYZhaOzYsQoLC6t0DkVF\nl24+UdRanp7NVFBwvqbLAFDP1Pd/VyoLSg492fKDDz6w/f3ixYtycnKSm5vbryri2LFjmjdvnlau\nXKnGjRtXuJ+Tk9OvGvdGDMOwGycqKkpRUVG2z+np6ZKuXb4JDw/X2rVrVVZWpqioKGVkZMjd3f2W\nawAAoCFwKEhI0sqVK7V06VKdOnVKknTPPffohRdesJ21uJmcnBwVFRUpMjLS1lZaWqo9e/ZozZo1\n2rp1q6RrZyZ++WryM2fOlDvj8EseHh4qLCy0a6usT1FRkZKTk7V8+XLl5OTI29tbFotFkuTt7a19\n+/apd+/eDs0JAICGzqEgsWjRIi1evFjDhw9Xly5dJElZWVmaO3euLl68qJEjR950jLCwMHXu3Nmu\n7dVXX1W7du304osvqn379vL09FRmZqb8/PwkScXFxcrKytIrr7xS4bgBAQHKzMzUCy+8YGvLzMxU\nYGDgDfefNWuWhgwZorZt2+rgwYN2d6OUlJSorKzspnMBAADXOBQk1qxZo7/85S96/PHHbW3BwcHy\n9vZWUlKSQ0HizjvvLLfGws3NTXfddZd8fHwkXXtexaJFi9ShQwe1a9dOCxculJubm91xhw4dKj8/\nP40fP97WZ/DgwVq8eLHCwsK0Y8cO7dq1S6tWrSpXQ2Zmpo4cOaIZM2ZIknx9fZWbm6udO3eqrKxM\nubm58vX1deQrAQAAcjBInDlz5ob/wfr5+ZW7rHArRowYoeLiYiUmJurcuXPy9/dXamqqmjZtatvn\nxIkTdpc+goKCbM+HSElJkZeXl5KSkuTv72839uXLl5WQkKCkpCQ5O1+766JVq1ZKSEjQtGnTZBiG\nEhMT1apVq9s2HwAA6jsnw4HnYEdGRio8PFyjR4+2a3/rrbe0bds2bd68ucoKrG3q+8rc+o67NlBb\nDZu1s6ZLwC1InVS/19bd8l0bL7/8ssaOHausrCwFBQXJyclJe/fu1Z49e5ScnHzbCgUAAHWLQ2//\n/N3vfqd169bJw8NDn3zyiXbu3CkPDw+tX7/+ps9dAAAA9ZfDt3927txZb775ZlXWAgAA6hiHzkgA\nAADcCEECAACYRpAAAACmESQAAIBpDgWJHTt2qLS0tKprAQAAdYxDd21MmDBBd9xxh5566ik9/fTT\n6tChQ1XXBQAA6gCHzkh8+umnevnll7Vnzx499thjioqK0saNG3Xp0qWqrg8AANRiDgWJpk2batCg\nQVq3bp22bNkif39/zZs3T6GhoZoyZYpycnKquk4AAFAL/erFlh07dtTzzz+vgQMHqqSkRB9//LGe\ne+45DRgwQAcPHqyKGgEAQC3lcJC4HhqGDx+uRx99VF988YUSEhKUmZmpnTt3ql27doqLi6vKWgEA\nQC3j0GLLv/zlL9q6daucnJz05JNP6tVXX1XHjh1t211dXRUXF6fevev3288AAIA9h4LEkSNHNHXq\nVPXp00eNGze+4T4tW7bU8uXLb2txAACgdnPo0sbo0aMVHh5eLkRcvXpVe/bskSS5uLioW7dut79C\nAABQazkUJKKjo3Xu3Lly7efPn1d0dPRtLwoAANQNDgUJwzDk5ORUrv3HH39UkyZNbntRAACgbqh0\njcSoUaMkSU5OTvrzn/+sRo0a2baVlZXp8OHDCgwMrNoKAQBArVVpkGjevLmka2ck7rzzTrm6utq2\nNWrUSF26dNGAAQOqtkIAAFBrVRokZs6cKUm69957NWzYMLm5uVVLUQAAoG5w6PbP0aNHV3UdAACg\nDqowSERGRmrFihW66667FBkZWekgW7Zsue2FAQCA2q/CIPHL50aEh4dXW0EAAKDuqDBI/PJyBpc2\nAADAjfzqt38CAABcV+kaCUexRqL+GDZrZ02XgFuQOokX5wGoXpWukQAAAKiMQ2skAAAAboQ1EgAA\nwDSeIwEAAEzjORIAAMA0niMBAABMc+hdG9cdP35cR48elSRZLBbdd999VVIUAACoGxwKEkVFRZo8\nebJ27typ3/zm2vpMwzD08MMPa8aMGbbXjQMAgIbFobs2pkyZouPHj2vlypX6xz/+oX/84x9asWKF\n8vPzFR8f79CBVq5cqcjISAUFBSkoKEh/+MMf9Mknn9i2G4ahlJQUhYaGys/PT0OGDNHhw4dvOm5G\nRoYiIiLUuXNnRUREaPv27Xbbly1bppCQEAUHBys1NdVu2/79+xUeHq7Lly87NAcAAGDPoSDx6aef\n6i9/+Yu6dOkiFxcXubi4qEuXLkpMTNSnn37q0IFatWqlCRMmaNOmTdq4caMefPBBvfTSSzp48KAk\naenSpUpNTVV8fLw2bNigFi1aKCYmRhcuXKhwzOzsbMXFxSkyMlLp6emKjIzUmDFjtG/fPknSwYMH\ntWDBAs2dO1fz5s3T/PnzdejQIUlSaWmppkyZomnTpsnV1dWhOQAAAHsOBYkWLVqoSZMm5dqbNGmi\nu+++26EDhYWFqVevXvL29lb79u0VFxenO+64Qzk5OTIMQ8uXL9fIkSMVHh4uHx8fzZ49WxcvXtTW\nrVsrHDMtLU3du3dXbGysLBaLYmNj1a1bN6WlpUmSjh07JqvVquDgYAUHB8tqterYsWO2vj4+PgoJ\nCXGofgAAUJ5DayT++Mc/asaMGXrjjTfUqlUrSdKpU6c0a9YsvfTSS7/6oKWlpfr73/+uS5cuKTAw\nUPn5+SooKFCPHj1s+7i6uqpr167Kzs7WoEGDbjhOTk6OBg8ebNcWGhqqlStXSpKsVqvy8vJ08uRJ\nGYahvLw8+fj4KD8/XytWrNDGjRt/de3Nm7vJxcX5V/cDqoOnZ7OaLgFokBryb8/hl3bl5+erd+/e\ndkGicePGOnPmjAYMGODQwQ4dOqRBgwapuLhYbm5ueuutt2S1WvXll19Kkjw8POz2d3d31+nTpysc\nr7CwsFwfDw8PFRQUSLp2Z0lcXJxiYmIkSePGjZPFYtHw4cMVFxenvXv3Kjk5WYZhaOzYsQoLC7vp\nHIqKLjk0V6AmFBScr+kSgAapvv/2KgtK1frSrvbt2+vDDz/UTz/9pG3btmnixIn64IMPbNudnJxu\n+RiGYdiNExUVpaioKNvn9PR0SVJISIjCw8O1du1alZWVKSoqShkZGXJ3d7/lGgAAaCiq9aVdjRs3\nlre3tyTJ19dXX331ld5//33FxsZKkgoKCtS6dWvb/mfOnCl3xuGXPDw8VFhYaNdWWZ+ioiIlJydr\n+fLlysnJkbe3tywWiyTJ29tb+/btU+/evIYZAABH1ehLu8rKynTlyhW1bdtWnp6eyszMtG0rLi5W\nVlaWAgMDK+wfEBBg10eSMjMzK+wza9YsDRkyRG3btpVhGLp69aptW0lJicrKym5xRgAANCwOLba8\ncuWKFi1apI8++kgnT560+w9Ykg4cOHDTMd588009/PDDuueee2x3Y+zevVuLFy+Wk5OToqOjtWjR\nInXo0EFsI2gAAAAXkklEQVTt2rXTwoUL5ebmpscff9w2xtChQ+Xn56fx48dLkqKjozV48GAtXrxY\nYWFh2rFjh3bt2qVVq1aVO35mZqaOHDmiGTNmSLp2RiQ3N1c7d+5UWVmZcnNz5evr68jXAQAA/j+H\ngkRycrL+9re/aeTIkZo5c6ZeeeUVff/99/roo480ZswYhw5UWFioP//5zyooKFCzZs1ktVq1dOlS\n9ezZU5I0YsQIFRcXKzExUefOnZO/v79SU1PVtGlT2xgnTpywu/QRFBRkez5ESkqKvLy8lJSUJH9/\nf7tjX758WQkJCUpKSpKz87U7Llq1aqWEhARNmzZNhmEoMTHRtpAUAAA4xskwDONmO/Xu3Vuvvfaa\nHnroIQUGBio9PV333XefVq1apS+++EILFiyojlprhfq+MnfYrJ01XQJuQeok1vjUVfz26rb6/tur\n7K4Nh9ZInDlzRh07dpQk3XHHHfrpp58kST179nT4yZYAAKD+cShItG7d2vY8h/vuu88WHnJycni8\nNAAADZhDayT69Omjzz//XAEBAYqOjtb48eO1bt06nT59WsOHD6/qGgEAQC3lUJC4fpeEJPXt21f3\n3HOPsrOz1a5dOz3yyCNVVhwAAKjdHAoS/yogIEABAQG3uxYAAFDHOBwkvvnmG6WlpenIkSOSrr3H\n4vnnn1enTp2qrDgAAFC7ObTYcvPmzXrmmWdUUFCgXr16qVevXraXdV1/dwUAAGh4HDojMX/+fI0Z\nM0ajRo2ya1+8eLGSk5P15JNPVklxAACgdnPojMTZs2f1+9//vlx73759debMmdteFAAAqBscChLd\nu3fX7t27y7Xv3r1bXbt2ve1FAQCAuqHCSxvbtm2z/f2hhx7S3Llz9dVXX9nu1sjJydH27dur5HXj\nAACgbqgwSPzpT38q17Zu3TqtW7fOrm369Ol67rnnbn9lAACg1qswSBw8eLA66wAAAHWQQ2skAAAA\nbsThB1J98sknWrp0qY4cOSInJyd17NhRI0aMUK9evaqyPgAAUIs5dEZi/fr1Gj16tO677z5NmDBB\n48ePV9u2bfXSSy9pw4YNVV0jAACopRw6I7F06VJNmjRJgwcPtrUNGDBAnTp10tKlS/XMM89UWYEA\nAKD2cuiMxMmTJ9WzZ89y7Q899JC+//77214UAACoGxwKEm3atNFnn31Wrv3TTz/Vvffee9uLAgAA\ndYNDlzaGDRum6dOna//+/QoMDJSTk5P27t2r9PR0xcfHV3WNAACglnIoSAwaNEju7u5KTU3V9u3b\nJUkdOnTQ/PnzFRYWVqUFAgCA2uumQeLq1av67LPP9MADD6hPnz7VURMAAKgjbrpGwsXFRaNHj9bF\nixerox4AAFCHOLTY8t///d91/Pjxqq4FAADUMQ4FidGjR2vWrFnasWOHfvjhB/344492fwAAQMPk\n0GLLF198UdK1QOHk5GRrNwxDTk5OOnDgQNVUBwAAajWHgkRaWppdgAAAAJAcDBLdu3ev6joAAEAd\nVOkaiZ9//lkJCQnq2bOngoODNX78eJ09e7a6agMAALVcpUFiwYIF2rRpkx5++GE99thj+uyzz/Ta\na69VU2kAAKC2q/TSxvbt2/X666/rsccekyQ98cQTioqKUmlpqZydnaulQAAAUHtVekbin//8px54\n4AHbZz8/Pzk7O+v06dNVXhgAAKj9Kg0SpaWlatSokV2bs7Ozrl69WqVFAQCAuqHSSxuGYejPf/6z\nXZi4cuWK4uPj5erqamtbtGhR1VUIAABqrUqDRL9+/cq1PfHEE1VWDAAAqFsqDRIzZ868bQdavHix\ntm3bptzcXDVu3FgBAQEaN26cfHx8bPsYhqG33npLa9eu1U8//SR/f39NnTpV999/f6VjZ2RkKDk5\nWcePH9d9992nuLg4uzeVLlu2TMuWLZNhGBoxYoSGDRtm27Z//37FxcUpPT3d7iwLAAC4OYfetXE7\n7N69W88++6zWrFmjtLQ0OTs7KyYmxu5dHUuXLlVqaqri4+O1YcMGtWjRQjExMbpw4UKF42ZnZysu\nLk6RkZFKT09XZGSkxowZo3379kmSDh48qAULFmju3LmaN2+e5s+fr0OHDkm6tgZkypQpmjZtGiEC\nAAATqi1ILFu2TE8//bR8fHxktVo1Z84cnT17Vl9++aWka2cjli9frpEjRyo8PFw+Pj6aPXu2Ll68\nqK1bt1Y4blpamrp3767Y2FhZLBbFxsaqW7duSktLkyQdO3ZMVqtVwcHBCg4OltVq1bFjx2x9fXx8\nFBISUvVfAAAA9VC1BYl/dfHiRZWVlenOO++UJOXn56ugoEA9evSw7ePq6qquXbsqOzu7wnFycnLs\n+khSaGiorY/ValVeXp5Onjyp77//Xnl5efLx8VF+fr5WrFihiRMnVsHsAABoGBx610ZVeP311/Xb\n3/5WgYGBkqSCggJJkoeHh91+7u7ulT63orCwsFwfDw8P23gWi0VxcXGKiYmRJI0bN04Wi0XDhw9X\nXFyc9u7dq+TkZBmGobFjxyosLKzSups3d5OLCw/jQu3k6dmspksAGqSG/NurkSAxc+ZM7d27V6tX\nry73hMzb8ZbR6683vy4qKkpRUVG2z+np6ZKkkJAQhYeHa+3atSorK1NUVJQyMjLk7u5e4dhFRZdu\nuT6gqhQUnK/pEoAGqb7/9ioLStV+aWPGjBn66KOPlJaWJi8vL1u7p6enpP87M3HdmTNnyp1x+CUP\nDw8VFhY63KeoqEjJyclKSEhQTk6OvL29ZbFYdP/998vb29u2SBMAANxctQaJ6dOna+vWrUpLS5PF\nYrHb1rZtW3l6eiozM9PWVlxcrKysLNvljxsJCAiw6yNJmZmZFfaZNWuWhgwZorZt28owDLundJaU\nlKisrMzM1AAAaJCq7dJGQkKC0tPT9fbbb+vOO++0nXlwc3PTHXfcIScnJ0VHR2vRokXq0KGD2rVr\np4ULF8rNzU2PP/64bZyhQ4fKz89P48ePlyRFR0dr8ODBWrx4scLCwrRjxw7t2rVLq1atKldDZmam\njhw5ohkzZkiSfH19lZubq507d6qsrEy5ubny9fWthm8DAID6odqCxPX/2J9//nm79tGjR+vll1+W\nJI0YMULFxcVKTEzUuXPn5O/vr9TUVDVt2tS2/4kTJ9S6dWvb56CgINvzIVJSUuTl5aWkpCT5+/vb\nHefy5ctKSEhQUlKSbV1Gq1atlJCQoGnTpskwDCUmJqpVq1ZVMX0AAOolJ8MwjJouoi6p7wtqhs3a\nWdMl4BakTupd0yXAJH57dVt9/+3VqsWWAACg/iBIAAAA0wgSAADANIIEAAAwjSABAABMI0gAAADT\nCBIAAMA0ggQAADCNIAEAAEwjSAAAANMIEgAAwDSCBAAAMI0gAQAATCNIAAAA0wgSAADANIIEAAAw\njSABAABMI0gAAADTCBIAAMA0ggQAADCNIAEAAEwjSAAAANMIEgAAwDSCBAAAMI0gAQAATCNIAAAA\n0wgSAADANIIEAAAwjSABAABMI0gAAADTCBIAAMA0ggQAADCNIAEAAEwjSAAAANMIEgAAwLRqDRJ7\n9uzRqFGj1LNnT1mtVv31r3+1224YhlJSUhQaGio/Pz8NGTJEhw8fvum4GRkZioiIUOfOnRUREaHt\n27fbbV+2bJlCQkIUHBys1NRUu2379+9XeHi4Ll++fOsTBACgganWIHHp0iX5+Pho8uTJcnV1Lbd9\n6dKlSk1NVXx8vDZs2KAWLVooJiZGFy5cqHDM7OxsxcXFKTIyUunp6YqMjNSYMWO0b98+SdLBgwe1\nYMECzZ07V/PmzdP8+fN16NAhSVJpaammTJmiadOm3bAeAABQuWoNEr169dK4cePUt29f/eY39oc2\nDEPLly/XyJEjFR4eLh8fH82ePVsXL17U1q1bKxwzLS1N3bt3V2xsrCwWi2JjY9WtWzelpaVJko4d\nOyar1arg4GAFBwfLarXq2LFjtr4+Pj4KCQmpukkDAFCP1Zo1Evn5+SooKFCPHj1sba6ururatauy\ns7Mr7JeTk2PXR5JCQ0NtfaxWq/Ly8nTy5El9//33ysvLk4+Pj/Lz87VixQpNnDixaiYEAEAD4FLT\nBVxXUFAgSfLw8LBrd3d31+nTpyvsV1hYWK6Ph4eHbTyLxaK4uDjFxMRIksaNGyeLxaLhw4crLi5O\ne/fuVXJysgzD0NixYxUWFlZpnc2bu8nFxflXzw+oDp6ezWq6BKBBasi/vVoTJK5zcnK65TEMw7Ab\nJyoqSlFRUbbP6enpkqSQkBCFh4dr7dq1KisrU1RUlDIyMuTu7l7h2EVFl265PqCqFBScr+kSgAap\nvv/2KgtKtebShqenp6T/OzNx3ZkzZ8qdcfglDw8PFRYWOtynqKhIycnJSkhIUE5Ojry9vWWxWHT/\n/ffL29vbtkgTAADcXK0JEm3btpWnp6cyMzNtbcXFxcrKylJgYGCF/QICAuz6SFJmZmaFfWbNmqUh\nQ4aobdu2MgxDV69etW0rKSlRWVnZLc4EAICGo1ovbVy8eFHHjx+XJJWVlenkyZM6cOCA7rrrLrVp\n00bR0dFatGiROnTooHbt2mnhwoVyc3PT448/bhtj6NCh8vPz0/jx4yVJ0dHRGjx4sBYvXqywsDDt\n2LFDu3bt0qpVq8odPzMzU0eOHNGMGTMkSb6+vsrNzdXOnTtVVlam3Nxc+fr6VsM3AQBA/VCtQeLr\nr79WdHS07XNKSopSUlLUr18/zZo1SyNGjFBxcbESExN17tw5+fv7KzU1VU2bNrX1OXHihFq3bm37\nHBQUZHs+REpKiry8vJSUlCR/f3+7Y1++fFkJCQlKSkqSs/O1xZKtWrVSQkKCpk2bJsMwlJiYqFat\nWlXxtwAAQP3hZBiGUdNF1CX1fUHNsFk7a7oE3ILUSb1rugSYxG+vbqvvv706sdgSAADUPQQJAABg\nGkECAACYRpAAAACmESQAAIBpBAkAAGAaQQIAAJhGkAAAAKYRJAAAgGkECQAAYBpBAgAAmEaQAAAA\nphEkAACAaQQJAABgGkECAACYRpAAAACmESQAAIBpBAkAAGAaQQIAAJhGkAAAAKYRJAAAgGkECQAA\nYBpBAgAAmEaQAAAAphEkAACAaQQJAABgGkECAACYRpAAAACmESQAAIBpBAkAAGAaQQIAAJhGkAAA\nAKYRJAAAgGkECQAAYBpBAgAAmFYrg8TKlSvVu3dv+fr6qn///srKyqp0/927d6t///7y9fXVo48+\nqtWrV9tt37x5s3r16qVu3bpp5syZdttOnTql3r17q7Cw8LbPAwCA+q7WBYmPP/5YM2bM0KhRo/Th\nhx8qMDBQI0aM0MmTJ2+4/4kTJzRy5EgFBgbqww8/1Isvvqjp06crIyNDknT27FlNmTJFEydO1Lvv\nvqvNmzfrv//7v239ExISFBsbKw8Pj2qZHwAA9UmtCxLvvfee+vXrp4EDB8pisSg+Pl6enp7lzjJc\nt2bNGrVs2VLx8fGyWCwaOHCgnnrqKaWmpkqS8vPz1axZM0VERMjPz0/du3fX0aNHJUkZGRk6f/68\nnnnmmWqbHwAA9UmtChJXrlzRN998ox49eti19+jRQ9nZ2Tfsk5OTU27/0NBQff311yopKZG3t7d+\n/vln7d+/Xz/++KO++uorWa1WnT9/XnPmzFFiYqKcnJyqbE4AANRnLjVdwC8VFRWptLS03GUGd3d3\nZWZm3rBPYWGhgoOD7do8PDx09epVFRUVqWXLlpo9e7YmTpyoy5cv66mnnlLPnj01depUDRgwQEVF\nRRo/frx+/vlnRUdHKyoqqtIaPT2b3doka7ktc5+s6RKABonfHuqqWhUkrrvRGYLKzhr86zbDMOza\n+/Tpoz59+ti2Z2VlKScnRxMnTlTfvn01e/ZsdezYUU888YSCgoJktVpvxzQAAKj3atWljebNm8vZ\n2VkFBQV27WfOnKlwMaSHh0e5Oy7OnDkjFxcX3X333eX2v3Llil577TUlJibqxIkTKikpUUhIiFq2\nbKlu3bpp9+7dt29CAADUc7UqSDRu3FidOnUqdxkjMzNTgYGBN+wTEBBww/07d+6sRo0aldt/0aJF\nevDBBxUQECDDMFRaWmrbVlJSYvcZAABUrlYFCUmKiYnRpk2btH79eh09elTTp0/X6dOnNWjQIEnS\nK6+8oldeecW2/6BBg3Tq1Cm9/vrrOnr0qNavX69NmzZp2LBh5cY+cuSItmzZorFjx0qS2rdvL2dn\nZ61evVpZWVn64osv1KVLl+qZKAAA9UCtWyMRERGhoqIiLVy4UKdPn5aPj4+WLFmie++9V5L0ww8/\n2O3v5eWlJUuWaObMmVq9erVatmypyZMnKzw83G4/wzAUHx+vV199VU2bNpUkubq62u7cOH/+vEaN\nGiVfX9/qmSgAAPWAk3F9ZSIAAMCvVOsubQAAgLqDIAEAAEwjSAAAANNq3WJL4Hb55z//qdWrV+vL\nL79UYWGhnJyc5O7urqCgIA0aNEitW7eu6RIBoM5jsSXqpaysLI0YMUItW7ZUjx495O7uLsMwdPbs\nWX322WcqKCjQ0qVLud0XqAE//PCDFixYoJkzZ9Z0KbgNCBKol/r376+goCBNmTLlhtunT5+u7Oxs\nbdy4sZorA3Dw4EH169dPBw4cqOlScBtwaQP10pEjR/Tmm29WuD0qKkrr1q2rxoqAhuPDDz+sdPvJ\nkyerqRJUB4IE6iVPT099+eWX6tChww23f/nll/L09KzmqoCGYdKkSWrSpEmF2zkRXr8QJFAvDRs2\nTK+99pr+8Y9/2NZIODk5qbCwUJ999pk2bdqk//zP/6zpMoF6qWXLlpoyZYp+97vf3XD7gQMH1L9/\n/2quClWFIIF66bnnnlPz5s31/vvva+PGjbaXsTk7O6tTp06aPXu2IiIiarhKoH7q1KmTvvnmmwqD\nhJOTE2cl6hEWW6LeKykpUVFRkaRrr6q/0VthAdw+WVlZunjxonr16nXD7ZcuXdLXX3+tbt26VXNl\nqAoECQAAYBpPtgQAAKYRJAAAgGkECQAAYBp3bQCoNpMmTdKmTZskSS4uLrrzzjvVsWNH9e3bVwMH\nDmQhLFAHESQAVKuQkBDNmTNHZWVlOnv2rL744gstWLBA6enpev/99+Xm5lYlx71y5YoaN25cJWMD\nDRmXNgBUq8aNG8vT01OtWrXSb3/7W8XExOiDDz7Q/v379e6770qSzp07p4kTJ6pr167y8/PT888/\nr8OHD9uNs23bNkVGRqpz587q1auXFi5caPdsgt69eyslJUWvvvqqHnjgAU2YMKFa5wk0FAQJADXO\nx8dHoaGh2rZtm6Rrl0D27dund955R+vXr5erq6teeOEFXb58WZL09ddfa8yYMerTp4+2bNmi8ePH\na8mSJVqxYoXduO+99546dOigjRs3aty4cdU+L6Ah4NIGgFqhY8eO+vzzz5WXl6edO3dqxYoV6tq1\nqyTpjTfe0MMPP6wtW7ZowIABeu+999S1a1f96U9/kiS1b99e3333nZYuXaohQ4bYxuzWrZtGjBhR\nI/MBGgrOSACoFQzDkJOTk44eParf/OY3CggIsG1r1qyZfHx8dOTIEUnSsWPHFBQUZNe/S5cuOnXq\nlC5cuGBr69y5c/UUDzRgBAkAtcLRo0fl5eVV6TsYnJycJP1f6LiZyt5ACeD2IEgAqHHffvut/vd/\n/1fh4eHq2LGjysrKlJOTY9t+4cIFffvtt7JYLJIki8WivXv32o2xd+9e3XPPPWratGm11g40dAQJ\nANXqypUrKigo0KlTp3Tw4EG99957GjJkiDp16qRhw4apXbt2evTRRzV16lRlZWXp0KFDmjBhgpo2\nbarIyEhJ114Tv2fPHqWkpCg3N1ebN29WamqqXnjhhRqeHdDwsNgSQLXKzMxUaGionJ2dbWsfRo8e\nrT/84Q+25zzMnDlTM2bMUGxsrIqLixUUFKR3331Xrq6ukq69pjo5OVkpKSlavHix3N3dNXLkSA0e\nPLgmpwY0SLz9EwAAmMalDQAAYBpBAgAAmEaQAAAAphEkAACAaQQJAABgGkECAACYRpAAAACmESQA\nAIBp/w+79irkQT1BdAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f0075eac208>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"(monty_df.groupby('prize')\n",
" .size()\n",
" .div(monty_df.shape[0])\n",
" .plot(kind='bar', ax=ax));\n",
"\n",
"ax.set_xlabel(\"Door\");\n",
"ax.yaxis.set_major_formatter(pct_formatter);\n",
"ax.set_ylabel(\"Probability of prize\");"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"image/png": 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0uE9RUZGSk5OVkJCgnJwceXt7y2Kx6P7775e3t7f27dt3i7MCAKBh+VVB4uzZs9q3b5+u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\nAIBp/w+79irkQT1BdAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f0075eac208>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"Of course this result can be derived analytically, but it is always a good idea to check our computations on cases where exact answers are known."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<style type=\"text/css\">\n",
".reveal blockquote { \n",
" text-align: left; \n",
" width: 85%; \n",
" border: none; \n",
" box-shadow: none; \n",
" background: none; \n",
"}\n",
"</style>\n",
"\n",
"<center><img src=\"https://raw.githubusercontent.com/pymc-devs/pymc3/master/docs/pymc3_logo.jpg\" width=\"500\"></center>\n",
"\n",
"From the [PyMC3 documentation](http://pymc-devs.github.io/pymc3/):\n",
"\n",
"> PyMC3 is a Python package for Bayesian statistical modeling and Probabilistic Machine Learning which focuses on advanced Markov chain Monte Carlo and variational fitting algorithms. Its flexibility and extensibility make it applicable to a large suite of problems.\n",
"\n",
"[![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://opensource.org/licenses/Apache-2.0)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"<center><img src=\"https://numfocus.wpengine.com/wp-content/uploads/2017/03/1457562110.png\"></center>\n",
"\n",
"As of October 2016, PyMC3 is a [NumFOCUS fiscally sponsored project](https://www.numfocus.org/blog/numfocus-announces-new-fiscally-sponsored-project-pymc3/)."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### PyMC3 features\n",
"\n",
"* Uses [Theano](http://deeplearning.net/software/theano/) as a computational backend\n",
" * Automated differentiation, dynamic C compilation, GPU integration\n",
"* Implements Hamiltonian Monte Carlo and [No-U-Turn sampling](https://arxiv.org/abs/1111.4246)\n",
"* High-level GLM (`R`-like syntax) and Gaussian process specification\n",
"* Provides a framework for [operator variational inference](https://arxiv.org/abs/1610.09033)\n",
" * Implements [ADVI](https://arxiv.org/abs/1603.00788) and [SVGD](https://arxiv.org/abs/1608.04471)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"To produce an interesting NUTS animation, we simulate a linear regression data set and animate samples from the posteriors of the regression coefficients."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"x_ani = np.linspace(0, 1, 100)\n",
"y_ani = 1 - 2 * x_ani + np.random.normal(0., 0.25, size=100)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
"image/png": 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MQ3avRNXtgKYU3j5oeROUzYl1qZ3jPb4/EfkOE+WoCe6AJj/ebDXryf7zjRPr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\npBL/H6I1rhLNHKv3AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f00768cd048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.scatter(x_ani, y_ani, c=blue);\n",
"\n",
"ax.set_title('MCMC Animation Data Set');"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using ADVI...\n",
"Average Loss = 20.537: 7%|▋ | 13953/200000 [00:02<00:29, 6348.40it/s]\n",
"Convergence archived at 14000\n",
"Interrupted at 14,000 [7%]: Average Loss = 55.812\n",
"100%|██████████| 1050/1050 [00:05<00:00, 180.45it/s]\n"
]
}
],
"source": [
"with pm.Model() as ani_model:\n",
" intercept = pm.Normal('intercept', 0., 10.)\n",
" slope = pm.Normal('slope', 0., 10.)\n",
" \n",
" tau = pm.Gamma('tau', 1., 1.)\n",
" \n",
" y_obs = pm.Normal('y_obs', intercept + slope * x_ani, tau=tau,\n",
" observed=y_ani)\n",
" \n",
" ani_trace_ = pm.sample(1050, tune=1000)\n",
" \n",
"ani_trace = ani_trace_[1000:]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"ani_cov = np.cov(ani_trace['intercept'], ani_trace['slope'])\n",
"\n",
"ani_sigma, ani_U = np.linalg.eig(ani_cov)\n",
"ani_angle = 180. / np.pi * np.arccos(np.abs(ani_U[0, 0]))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
"image/png": 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qWxNREEWmD59Shbtw/SLj08eRdDfmg8oIPsjQ6DTNRp1KeWuTORFdol6rrPfO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\nhscboNNu4XB5lSSGm0Ia+/0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"text/plain": [
"<matplotlib.figure.Figure at 0x7f00517d17f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ani_fig = plt.figure(figsize=(4, 3))\n",
"\n",
"e = Ellipse((ani_trace['intercept'].mean(), ani_trace['slope'].mean()),\n",
" 2 * np.sqrt(5.991 * ani_sigma[0]), 2 * np.sqrt(5.991 * ani_sigma[1]),\n",
" angle=ani_angle, zorder=5)\n",
"e.set_alpha(0.5)\n",
"e.set_facecolor(blue)\n",
"e.set_zorder(9);\n",
"\n",
"ani_images = [(plt.plot(ani_trace['intercept'][-(iter_ + 1):],\n",
" ani_trace['slope'][-(iter_ + 1):],\n",
" '-o', c='k', alpha=0.5, zorder=10)[0],)\n",
" for iter_ in range(50)]\n",
"\n",
"ani_ax = ani_fig.gca()\n",
"ani_ax.add_artist(e);\n",
"\n",
"ani_ax.set_xticklabels([]);\n",
"ani_ax.set_xlim(0.9, 1.25);\n",
"\n",
"ani_ax.set_yticklabels([]);\n",
"ani_ax.set_ylim(-2.5, -1.9);\n",
"\n",
"mcmc_ani = ArtistAnimation(ani_fig, ani_images,\n",
" interval=100, repeat_delay=5000,\n",
" blit=True)\n",
"mcmc_video = '<center>{}</center>'.format(mcmc_ani.to_html5_video())"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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"\">\n",
" Your browser does not support the video tag.\n",
"</video></center>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"HTML(mcmc_video)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Statistical workflow\n",
"\n",
"1. Tell a story about how the data may have been generated\n",
"2. Encode that story as a probabilistic model\n",
"3. Perform inference\n",
"4. Check model diagnostics\n",
"5. Compare models\n",
"6. Iterate (`GOTO 1`)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"#### Statistical LEGOs\n",
"\n",
"<center><img src=\"http://austinrochford.com/resources/talks/img/stat_legos.png\" width=\"900\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Case study: NBA foul calls\n",
"\n",
"<center><img src=\"https://upload.wikimedia.org/wikipedia/commons/2/2d/Tom_Washington%2C_Monty_McCutchen%2C_Brent_Barnaky_on_March_30%2C_2011.jpg\" width=\"750\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"The foul calls data set was derived from the NBA's [Last Two Minute Report](http://official.nba.com/nba-last-two-minute-reports-archive/) by [Russell Goldenberg](http://russellgoldenberg.com/) of [The Pudding](https://pudding.cool/). The data set, along with the code used to scrape and parse it is [available](https://github.com/polygraph-cool/last-two-minute-report) on GitHub.\n",
"\n",
"The Pudding has published two [very](https://pudding.coo/2017/02/two-minute-report/) [interesting](https://pudding.cool/2017/03/home-court/) visual essays using this data that you should definitely explore.\n",
"\n",
"I have also [written](http://austinrochford.com/posts/2017-04-04-nba-irt.html) about using this data set to understand and quantify player skill in drawing/committing fouls."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"NBA_DATA_URI = 'https://raw.githubusercontent.com/polygraph-cool/last-two-minute-report/master/output/all_games.csv'\n",
"\n",
"nba_df = (pd.read_csv(NBA_DATA_URI,\n",
" usecols=['seconds_left', 'review_decision',\n",
" 'period', 'date',\n",
" 'away', 'home',\n",
" 'score_away', 'score_home',\n",
" 'disadvantaged_team', 'committing_team'],\n",
" parse_dates=['date'])\n",
" # the report contains data from the last two minutes of the fourth\n",
" # quarter and overtime periods; for simplicity, we focus on plays in\n",
" # the fourth quarter\n",
" .where(lambda df: df.period == \"Q4\")\n",
" .dropna(subset=['period'])\n",
" .drop('period', axis=1)\n",
" # we restrict our attention to the 2016-2017 regular season\n",
" .where(lambda df: df.date.between(datetime.datetime(2016, 10, 25),\n",
" datetime.datetime(2017, 4, 15)))\n",
" .dropna(subset=['date'])\n",
" .drop('date', axis=1)\n",
" # empty review decisions should be incorrect non calls\n",
" .assign(review_decision=lambda df: df.review_decision.fillna(\"INC\"))\n",
" .dropna()\n",
" .reset_index(drop=True))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Last two minute report"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>seconds_left</th>\n",
" <th>review_decision</th>\n",
" <th>away</th>\n",
" <th>home</th>\n",
" <th>score_away</th>\n",
" <th>score_home</th>\n",
" <th>disadvantaged_team</th>\n",
" <th>committing_team</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>111.0</td>\n",
" <td>INC</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" <td>104.0</td>\n",
" <td>113.0</td>\n",
" <td>POR</td>\n",
" <td>UTA</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>102.0</td>\n",
" <td>CNC</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" <td>104.0</td>\n",
" <td>113.0</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>98.0</td>\n",
" <td>CC</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" <td>104.0</td>\n",
" <td>113.0</td>\n",
" <td>POR</td>\n",
" <td>UTA</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>64.0</td>\n",
" <td>CNC</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" <td>104.0</td>\n",
" <td>113.0</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>62.0</td>\n",
" <td>INC</td>\n",
" <td>UTA</td>\n",
" <td>POR</td>\n",
" <td>104.0</td>\n",
" <td>113.0</td>\n",
" <td>POR</td>\n",
" <td>UTA</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" seconds_left review_decision away home score_away score_home \\\n",
"0 111.0 INC UTA POR 104.0 113.0 \n",
"1 102.0 CNC UTA POR 104.0 113.0 \n",
"2 98.0 CC UTA POR 104.0 113.0 \n",
"3 64.0 CNC UTA POR 104.0 113.0 \n",
"4 62.0 INC UTA POR 104.0 113.0 \n",
"\n",
" disadvantaged_team committing_team \n",
"0 POR UTA \n",
"1 UTA POR \n",
"2 POR UTA \n",
"3 UTA POR \n",
"4 POR UTA "
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nba_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"# there are a few typos in team names; this dictionary corrects them\n",
"TEAM_MAP = {\n",
" \"NKY\": \"NYK\",\n",
" \"COS\": \"BOS\",\n",
" \"SAT\": \"SAS\"\n",
"}\n",
"\n",
"def correct_team_name(col):\n",
" def _correct_team_name(df):\n",
" return df[col].apply(lambda team_name: TEAM_MAP.get(team_name, team_name))\n",
" \n",
" return _correct_team_name\n",
"\n",
" # correct typos in team names \n",
"df = (nba_df.assign(away=correct_team_name('away'),\n",
" home=correct_team_name('home'),\n",
" disadvantaged_team=correct_team_name('disadvantaged_team'),\n",
" committing_team=correct_team_name('committing_team'))\n",
" # turn home and away team scores into committing and disadvantaged team scores\n",
" .assign(score_disadvantaged=lambda df: (df.score_away\n",
" .where(df.away == df.disadvantaged_team,\n",
" df.score_home)),\n",
" score_committing=lambda df: (df.score_away\n",
" .where(df.away == df.committing_team,\n",
" df.score_home)))\n",
" .assign(score_diff=lambda df: df.score_committing - df.score_disadvantaged)\n",
" .assign(foul_called=lambda df: 1 * (df.review_decision.isin(['CC', 'IC'])))\n",
" .assign(seconds_left=lambda df: df.seconds_left.round())\n",
" .drop(['away', 'home', 'score_away', 'score_home', 'review_decision'], axis=1))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Story\n",
"\n",
"Close basketball games usually end with intentional fouls."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
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Z8djcuXPxu9/9DoAgJBoaGtDc3Aye59HQ0IApU6agsbERL7zwAl599dV+e49D\nEVYVkvg3QWQCy68AgFgsPoh7QuQrTAyw5EOtDbKYqGWJl3a7XfMQsoFELiRyNSeEIQ+rpHMsqqpG\ng+M4tLUNXMmp5iFkueDYsWP47ne/K46q/dWvfoXa2lp89NFHAISaWznl5eVpG3B1dHQkLVNRUQGX\nywUAqKmpwcqVK7F06VIAwJ133omamhrccsstWLlyJQ4cOIANGzaA53nccccdSa5KKior87N3h8kE\nmM1Ck7OCAuOAvI98PVYDTT4ep/Z2Xvw+2WwD830C8vNYDQb5cJyMxjjMZiMmTz7n7Hcpqmm/LRbh\nXDZmTCUqK4tQUlKMzs7OlMtynLCd8eMrYTIpL3v9eZwmTRon/kZKSkowalTuhEV1daW47smTz0n7\nPqqrq+B2dwzYd2LAciwAYOLEidi+fTt6enqwa9cu/PSnP8Xzzz8vPp+L4SyJ42EXLlyIhQsXiv9+\n7bXXAACzZ89GXV0dXn75ZcTjcSxcuBA7d+7UlMjjcvVfTK4/6enxIRIRkuxaW939/j4qK4vy9lgN\nJPl6nM6caRO/T93dvgF5D/l6rAaafDlOLpcHkUgMwSAPg8GEzk6Ppv1ubu5AJBJDJMLB5eoFx5nQ\n3e1NuWxXVzd4noPbrXQ1+vs4RaMm8TdisxXmdFscZxHXHYuZ0667tLQChw9/hubmLpjN5oy2p0eU\nDFiOBQBYLBZMmDABAHDRRRfhk08+wXPPPSfmSLhcLkWr1c7OziRHQk5FRQU6OjoUj6Vbxu12Y8OG\nDdi2bRsOHTqECRMmoKamBgAwYcIEfPzxx7j66qs1vZd8RB7+oO6bRLbIQyGUY0FkAisvtdnsKCgo\n1JFjISVvAkKTq1gsikgkonrhDAaDugaI5Qp5KCRXPSwYrJdFcbEzyYVJpKqqGp999ina2loxbtz4\nnO6HGoOSY8GIx+MIh8MYN24cKisrUV9fj2nTpgEQKhj279+Pe+65J+XyF198Merr6/HDH/5QfKy+\nvh4zZqg3MVmzZg0WLVqEcePG4ejRo4qTYSQSQTw+vOPE8nJTqgohskWZY0HCQg+BQABbtz6DBQu+\nhbFjxw327gwa8jJQm82mWViw7x5L3mS5E4GAH2ZzcoJkMBiA1Trw1X9ms1nM/2BCIFew9Wlx2dkN\ne0tL84AIC819LLLliSeewP79+9HY2Ihjx45h7dq12LdvHxYsWACO47B48WI8/fTT2LVrF44fP457\n770XBQWGPDXmAAAgAElEQVQFuO6668R1LFmyBGvXrhX/vXjxYnz44YfYtGkTvvjiC2zatAl79+7F\nkiVLkrZfX1+PEydOYPHixQAEx+TUqVPYs2cPdu/ejVOnTuGiiy7q/wMxiMgbZFEfCyJbWA8LgKab\n6uXo0cPYufMv+Nvf3h/sXRlUmGNhtwuOhdYGWcyxYK3Apbbe6k5sMBgctLYCzKnIZUUIABQVCevT\nMop9oKecak7ejEaj+Oc//4mWlpakdtDf+ta3+ly+o6MDd999N1wuF4qKilBbW4vNmzfjyiuvBAAs\nW7YMoVAIq1evRnd3N6ZPn44tW7YoelicOXNGESqZOXMm1q1bh1/+8pfYuHEjxo8fj/Xr12P69OmK\nbQeDQaxatQrr168XJ7RWVVVh1apVeOCBB8DzPFavXo2qqiqthyMvIceCyCUUCskcNmF4pJd9B4NB\nWK1WcBwHu92OcDiMWCymmKT9zDObEI/HsWzZcvGx5HLT9PNCAoGAOOlzoHE6nWhtbem3UEi6ihCG\nvPvmQKBJWHzxxRdYvnw5GhsbwfM8jEYjotEoTCYTLBaLJmGxZs2atM9zHIcVK1ZgxYoVKV+zZ8+e\npMfmzZuHefPmpV23zWbDzp07kx6//vrrcf3116dddjihzLEgYUFkB4VCMoeJ/JEu8AOBgNg5U2rN\n7RdbVgPAu+/uQSgUwg9/eJuYmC8JCynHAlAXatFoFNFodBAdC8FZyFXXTUZNzVcwe/Zc/Mu/9J0X\nyETVkSNHkgoc+gNNoZBHHnkEU6dOxf79+2Gz2fDmm2/i1Vdfxfnnn4+NGzf26w4SuYENHjMaBS1J\nwoLIFmUohISFHpiwGCkhyXA4rJo/IQgLQVAw90E+iCwSicDr9SISiSgS9RP7WDDRoNZ9k4mNwUje\nBACns/Ts/3MrLCwWC+6++2eYOvXCPl/rcDhw+eWzcPLkiQEJv2kSFp9++imWL1+OgoICGAwGRKNR\nTJ06FXfffXefTgQxNIjFYuB5XrTPqCqEyBbmWAjnBMqx0APLdxopv8Nf/3oDbr/9R+B5XvF4IOAX\nL/hq4QyPxyP+3dLSJP7t9wvLGQyGs8umnhei1s57IGHhe70j13PN0qU/hNFowrZtz/b7jaUmYcHz\nvPihl5WVoa2tDYBwoNhwFWJow8IgLGeFxXgJIlN8Pi+sVissFgvicRIWemB5aiOlA+7Jk1+go8OF\n3t4e8TGe5xEKhWTCIlkceDxu8e+mJrmw8IkOh7CsVBWSyGC182bMn78Ajz76BCZN+sqgbJ9RVTUa\n3/jGt9DR4cL27f3bdVqTsJg8ebJYfjpt2jT89re/xb59+/Dkk0/inHP0j5IlBh5mvRYVCbHLkXKn\nRPQfPp8XhYUOmEympIRuIj3s96i1hXW+43Z3AVA6EFKpqdSWG5AqPoTlJGEhH6Ll9/vFMAggiQa1\nqpDBaufNsFqtOO+88wdl24l85zs3wekswR//+Ht0dnb223Y0CYvbbrtNtLDuuOMOtLS0YPHixfjg\ngw9w33339dvOEbmDORTMsRgpd0pE/+Hz+eBwOGA0mijHQifs9zcSkjfD4bAYNmPDuIDkUebMgVA6\nFl3i383NgmPB8zx8Pp9CWKSrCmFiY7ByLIYSBQUFWLRoCcLhMJ5//tl+246mqhBWEgoA48ePx5tv\nvgmPxwOn09nv2aVEbmB3SA6HkGMx0svchjvBYBAffbQfl112RZ9d+TKBndzHjz8HPp+PQiE6YQ7P\nSEiilrsO8r/lXTcBdXEgfz0TFoFAADzPo7BQakWQripksB2LocbVV38Nb775Bt577x382799A5Mn\nT8n5NjQ5Fi6XK6mxRklJCdra2pJaahNDE3aHZLfbYDSaRsSd0kjmvffewS9+8Sg+/vhgv6zf7/eD\n53k4HEUwmYyUvKkT9nscCQJfnich/5s5E+yCz8SBvHqEvd5ut6OtrQ2xWEx8njXHkq8jXVXIYOVY\nDDU4jsONNwoTw7WcH3iex65df9G1DU3C4p577sH77yeXqPz1r39N23KbGDqwOySz2QKr1TIi7pRG\nMixJrqenp49XZgaztgsLC2E0Uo6FXqLRkZO8yfIrAGWOBRMBLKQh9bEIyJYVhMV5512AeDyG9va2\npDkh8r/lpaqJ2yHHQmLUqFEAlKGpVLS0NOM3v/mVrvVrEhaffPIJLrnkkqTHL7nkEnz66ae6NkgM\nDuwEZrFYYLXaSFgMc9jn2193xKyHRWFhIUwmE4VCdDKSyk3l4Qxl8qYy9yGVY2EwGFBbex4AIRyS\n2HUTUM4KSYRyLJIpLha6gHZ3d/f5WvnnpxVNwiIWi6kq61AoNCIUd3/w4Yf1+OyzgRNlLMfCbDbD\nYiHHYrjDPt/+unBJjoVQFULJm/oYbg2yeJ7Hjh1vor29Pek5efhDmbwpzQkBJNchsdzU6SwRB2c1\nNzcnNccCpDAH5VhogzXrkgu9VMhLhLWiSVhMmzYNL730UtLjL7744rAf3NVfPPnkOmzZsnnAtsfu\nkCwWC2w2G+VYDHP627FgJ3eHwwGDwUjCQifshiwejw2LY1df/zds2vRrbN/+h6TnurrkoRC1HAv1\n5E2e5+F2u1FaWioO0WpubpTlWEjJmxaLBQaDQdWxoByLZMxmMwoLC9HT07djoeU1iWhKF1+5ciWW\nLFmCY8eO4YorrgAAfPjhhzhy5Aiefbb/SlaGKzzPIxgMZvSBZQoTEmazBRaLZUQkjY1k2OfdX84U\nExaFhYUwm02IxSgUogd5TkowGFQMW8xHdux4EwDE5olymJhwOBwJoRClY5EYCgkEAgiHwygpkYRF\nS0sLzj13EgClY8GGmJFjoZ3iYqemMEdvb2+fr0lEk2Nx8cUX4+WXX8a4cePw1ltvYdeuXRg3bhxe\nfvllzJw5U/dGRzqsvbZ81kJ/w6xXq1XIsYhGo4jH4wO2fWJgYSdYtSz5XCCFQopgNJrA8zx9n3Qg\nDyHnu3vY1NSITz/9JwCgvT1ZWHR1dcFisaC6egw8Ho/YE0ma4SHN++A4ThQcTJCUlJTCbrejtLTs\nrGORnLwpLG9X/b5TjoU6JSUl6O3t6fN3m4mw0Fzgft555+GJJ57QvQEiGXa3EgwGxSmx/Q0LhQhV\nIVYAULTTJYYX/V3OqKwKEUZcR6NRWCyWftnecIMJfSD/e1ns3CmUInIch/b2tqTpmR6PEM4oLS1F\nPB6D19uLoqJiWRKmXVzeZrOJIRLmbpSWCkO8xowZg8OHPxPvsuXJm4AgHNSSEaWW3uRYyCkudoLn\nefT29qQd6d5vjgWRW+QnFWYpD9Q25cIi3++UiNSwk2l/V4U4HA5RGA+HXIGBIjEUkq+EQiG8885u\nFBc7MWPGVxEOhxUhXp7n4fF4UFJSKk75ZIIhMccCEMSCmmMBAGPGjAPP8zh16iQAZR8Lth7KsdAO\nE2x9VYb0W/ImkVuYewAAXu/ACAup3NQsCovhkpFOJMNauPdfjoWyKgQAlZzqQB4KyWfHor7+b/B6\nvbjmmq9jzJixAKCoDOnp6UY8HkNJSal4IWOCQeq8KTkJdrtd7EXBnAm2HJsS+sUXnwNQdyyi0WiS\nwA0GA+A4jty0BJhL0Vcvi56ebt0dtklY6GTZsmVZiwG5YzFQwkLZIIsci+EOcyz6q9yUfW/loRBq\nkqUd+Tkgn3+HO3e+CY7j8PWvzxObLrlckrBg4qCsrEy8kDHHIjHHQvjbLoZI1BwLQHI6EnMs2ITT\nxDyLYDAo5m8QEomfRyp6e4XQlR5IWOjkxIkTaGw8k9U65CfggUrglDfIslikHAtieMIuVv1Zbsoy\n8aVQCDkWWpG7lvnqHDY0nMKxY0cxY8ZXUVU1GpWVVQCUCZxycVBSkigsAmJeBaOgoBCxWBSRSCTJ\nsRgzZoxi+8nCgvXBUH7nA4EAhUFUYL0s+g6F9IpTsbWSsbA4ffr0iL0wZZtpPxiOhVRuahZ/yCP1\n8xsJsItV/+VYeFFYWAiO42A0UihEL6ylN5C/3Td37hRKTOvq5gOAqmPBelgoHQsWCgkkOQnyDprs\ndWy50aOrxdfa7XYYDMrLF0tET+VYEEq0hEJY9WK/CIt169bhT3/6k7ihpUuXoq6uDnPnzsXHH3+s\na4PDgWxP1vK7lUwybrPZptVqFWON+XpCI/qm//tY+MQGRZS8qZ/hUG66d++HKC524qtfFcY9MGEh\nz7Fgc0KUORbChczv9yc5CfLR6W63G2azWXQmzGYzKisrFa+Tw9Yl79wJCEKDqt+SSXSQ1PD5vOB5\nvn9CIa+//jomTpwIAHj//fdx5MgRvPLKK/jmN785IktQE7+4ehn8qhBBvVM79uEJz/MD0NLbKxMW\nlGOhF/mxSrTu8wWfz4vKylFijk1hoQN2u101FFJWVibmSsgdi8QLPis99fl8Ypmq3NGorh579nXK\nMAigPi+ENSMkxyIZKRSSWliwIYb9Iiw6OjowevRoAMB7772Ha6+9FtOmTcOiRYtw5MgRXRscDmTr\nWAxujoUZVqvgWORzmRuRmlgsJja96Y+LViQSQTgcFrtFUihEH/LPB8hPxyIejyMcDsNms4qPcRyH\nUaOq4HK1i02wWCiENbkym82KHAt54iag7L7JylTlsDyLxFJTQH3WSDgcBs/zlGOhQmGh0I4/nbBg\njnq/hEJKSkrQ1NQEAPjggw/Ett7RaFT8Ao0kss+xGPhyU2VVCHMs8u+ERvSN/PsZiyWX32khXTc+\neTtvAJS8qRMm8uWN6vKNVL0hRo2qQiAQEL8jHo8bHMfB6SwBx3EoKSlBd7dHHGyZ7FgI4qC9vQ3x\neEwMnzBYZYh6KIQ5FtL3n9p5p0b4XJx9CAvBsSgu7gfHoq6uDnfddReWLl0Kj8eDK6+8EgBw9OhR\nTJgwQdcGhwPZ51gMRvImVYWMFFgPC4be7+tbb+3AzTf/u2JglBzWw8LhEO5i5J03ib5hYUlmL+ej\nc5jqgi3lWQjhELfbjaKiYvE74nSWwuPxJM0JYTDHoqWlGQCSHAvWy0LNsWDLyo8n+5vdTBFKSktL\n0+ZY9Ktjce+992LRokWoqanBs88+K6pKl8uFhQsX6trgcCCXORYDFQph2zSZTKJ9ScJieJKYV6H3\ncz59ugGBQACtra2qz8t7WACSYxGLkbDQQiQiHCd2ss5H55B9pxIv2JWVygROj8eNsrIy8fnS0lLE\nYlF0dHQASBYmTGg0NwsOeaKwmDhxEiwWC8aOHZe0T4nTUYW/A2efI2GhRnGxE6FQKKW4ZY6F3hwL\nTUMqTCYTfvCDHyQ9/v3vf1/XxoYLuawKGTjHIgKz2Xy2Ax0Ji+FM4ueqN4GTOQ9yASwndSiEhIUW\n2HFlya/56FikumCPGiX1sggGgwgEAigtlYQFEwqtrS1nl1fPsWCOhXxZACgrK8fmzc+lrQpRcywo\nx0IdVhnS3d2tGi7KNHkzpbD47LPPcP7558NgMOCzzz5Lu5KpU6fq2mi+k499LCKRsBjTJcdieJP4\nuer9vrJciVRVQ5JjwZI3KRSiB3ZcmWORj79Dts+JF2zmWLhc7UmdM4W/hQsZEw7JoZD0jgUg3GWr\nwUSO3LGgHIv0sGPZ09ONqqqqpOczDYWkFBY33HADPvjgA5SXl+OGG24Ax3GqiZocx424ypDc5lj0\nJk0D7A/C4TDMZqEahByL4U2ita63syMLaaQqH5VyLJR9LGIxSt7UAruxYDkq+fg71JJjIW+OxWBN\nmVpamGOhFBaFhYJjwY5JYvJmOqSKEnnyJjkW6WBCj3U5TSTT5M2UwuLtt98WvxBvv/22rpUOd7LP\nsWAVGmaxdI+5Cdny7rt7sGfPbtx//2rFOPZIJAKLxQwAVBWSJ3R0dODRR1fjRz9agZqayZqXY0LC\n4XDA6/XqDoUwgZDKsUgOhQjfK3IstMFCoZJjkX+hkFQ5FkVFxbBarWhvz9SxUIZG1ByLVKh13qQc\ni/QwodfTo57AyRwLJoK1klJYjB07VvXvkY7FYsmZY1FWVoa2tjZ4vd6cCYv6+r/hk08+RltbqyLB\nKRwOi6qT+ljkB4cPf4qTJ7/AwYMf6RIWTDAWFzvPCgt9ArLvHIvEqhCDYjkiPaydt8VigdlsTqri\nyQdSXbA5jkNl5Si4XO2iYyF3HZJzLNRDIdLrSzTvE+VY6Ic1yUpVGdLb26OYB6QVGkKmE7vdnnWO\nBTuxsB9ZJvPuU9HZ2QkA4oRARiQSFlt5U+fN/IDlMuht+87ugNlJQ6/DxkIh8iRjtf2iqpDMkJd+\nW63WrM8ng0G6Ms5Ro6rg8/nQ1CQMa1RzLDo7haqQVMmbgPD90jPq3Gq1guM4yrHQgTx5U42enh7d\nYRCAhIVuBGGRm6oQlvHM7gBzQVdX59l1KpNCQ6EwzGbBsqZZIfkB+wz1JviyO2CWmKXfsWChEPXl\n2H4ldt6kHAttyJvV2Wz2vAxJprtgszyL48ePAVDmWDCRwfL1Eh0Ki8UCg8GoeK1W2KRUciy043QK\nx1itSRbP8+jt7YHDQcKi38mFY8EsZvaDy9UgslgsJn5B5I6F0EI4JiZvCiWnlry0YEcSTFD4fJk5\nFkxY6K8KYY5F+qoQVvJHnTf1IW+vL4RW81FYpL5gs5LThoYGAEqBUFBQoLDVE5fnOE6cF6InDCJf\nn/zcRzkW6UkXCgmFQohGo+RYDAR2uz3r+QvsxCI5FrkRFm63W7wT8PslF4TdIcltRavVSo7FECfz\nUIhwoWInDb0Om5aqEJYfAEiOhXwU+HDl6NEjOHo0uyo4+UBAm82Wl79DSVioh0IAYXaMzWZTuBJC\nW29JaKhNHWWP6XUs2LLKlt7kWKSDTY/t6UkOhWRaagqQsNCN3W7PeP4Cg52AmWORq1AIG1EMKB0L\n6URmFh+zWm15acGOJDIPhUjJm/J/a4V9t1Mt5/P1ij0sAGm66UgIhWzYsBYbNqzNah0sFMpyLNig\nrHwinbBgvSwAdXHQt7AQ8iz0lJrKl5U7dFLIhoRFKpzOElXHordXEBuZCIuUqZ633Xab5pU89dRT\nujecr8hLmvSW4DAScyxyFQphiZuAUqzIT2QMi8WS09wOIvewz0evsGCCUXIs9CZvCgPI0lWFyC8O\nI6nzZne3RwwpZorUXt8Mi8UKnufPloNnt96BhLks6qEQSVjI8ysY8hBH7h0LG8LhMGKxGIxGY1oB\nRAg4nU60trYgHo/DYJC8hky7bgJpHIvS0lLN/40kpH70mduX7MTCfji5mhfCEjcBZfKm3Hpl2Gzk\nWAx1JMdC3/eDxeyZsNDrWKSrCuF5Hj6fT0zcBEZO8ibP8wgGgykFl1bkORbsgpdv4RAmVtVyF5zO\nEtEdVRMHrHeCsHxB0vMsdyeTa8u4ceMBADt2vHl2P0lY9IXTWSImasqRQiH6hUVKx+LRRx/VvbKR\ngFoTFr2Ew2EYjSbRqs5VW2+5sJCHQuQnMoaQvBkakK6fibS1taGjw4WpUy8c0O3mG0xYhMNhhMNh\nzXe0ycmbuZsVEggEwPN8QihkZDgWPp8PPM+nLMPVirwqhPWvCQZDyMBxHjSYeFUrN2W9LJqbm1TF\nAXMsWBJ5Itk4Fjfd9D387W/v44UXnsNll12BYDAAk8kktp0nkpGXnMpFHxMWlLw5AEjCIvM7jGg0\nCovFLN719Y+wkIdCkh0Lq9WGeDw+KBeDLVs24cEH/w/10egD+fdCj2vBjmumjkW6HAsWnmETjoGR\nJSwAwdHJJidC2ccifx0Lg8GYsnESS+BMl2Nht9tVb2qYaE0cQKaFkpJSfP/7tyAYDOLpp/9/BAIB\n1XALIcHERGLJqTTZNIc5FnL6yrcYqTkWmRIOh2EymWG1WmEymXIoLKTkTZ8v2bGQd/dk3TdDoaAi\nqXMgaGtrQzQaRSgUzKu48kASj8cVrpPX60VZWbmmZZnoZRam/hyL1FUhLHwmj62zzpvDvUFWoljP\ntFuuPJmarSPfwpLBYBA2mzWl28kSONVyLJiLoRYGAYDrrvsGqqqqcO65EzPat6uv/hreffcd7N+/\nDxzHoaKiIqP1jBQkYaGsDMlGWGhyLBJzKhwOB5qamrB//37KscgAeRdMh6MoZzkWnZ0dcDgcsFgs\nCeWm6lUhAAallwXLQM7WUh7OyD8/QN3V2rJlM5555umkx8PhEAwGI8zmzPokpJtuyu6smTAFRs6s\nEHmyczZ5FpGIcJxYVQigf1DcYBMMBtJWWkycOAkAMHbs+KTn2IUslZNwzjkTcMMN/55xiJbjOPzo\nRytgNpvB8zxVhPQBC4UkVoZIyZvq02TTocmxSJVvsWbNGrGt70ghN45FRDyhOBwO1a5nmeB2d6G8\nvAK9vb0JVSGS9cqQJpwOrAUbj8fFmumBvktj9vVA55RkQmLFjpqweOed3TAYjLjlllsVj4dCIfHC\nb7PZdX/G6XIspAoj6W59pDTIUvtNZYK8KiR/kzdDac/9X/taHWprazFp0leSnmMXsv684FdXj8FN\nN30PL7ywlRI3+yB1KGSQ+ljcdNNNePHFF7NZRd6RC2GhdCyECZTZ1rGHQiH4fD6UlpahoKAgoY+F\nlCzGsNkGZ3R6b2+P+F4HOsfinnvuxOOPPzKg28wU5mKx75vXq8zYjkaj8Hq9YkKhnFAoJJ60bTar\n7nygeFwQCGqhEHYBlItUlhg3kkIhqZqHaUGeTM1uMPJtdLrgWKS+YJtMJlVRAUg5FvI8nf7gm9/8\nNmbPnosrr7yqX7eT77BcrORQSC9MJlNGIT99I8sSOHXqVDaL5yXsx5RN8mY4HBYv8kVFxeB5Hn6/\nPyv3hyVulpdXwO/3obW1Vaz4UK8KGZwTmtvtFv8eSGHh9/tx4sRxnDhxHK2tLRg9unrAtp0J7O64\nunoMTp78IsmxYK5PLBZNiveHQiHFwDl54zQtpGvpzUJn8u1JnTeHt7DItWMhrwrJJ2EhVMaEM3YC\nHA4HbrnlPzFhwoQc75kSk8mEu+/+Wb9uYzggVYW4FY97vT0oLnZm5PBqEhYPPfSQ4t88z8PlcuH9\n99/HDTfcoHuj+YyUY5GZY8Ga4ZjNwqFnYsLr7c1KWLDmWGVlZejs7FBccNT6WAxW0pjcbhtIYdHe\n3ib+vXv3Ltx885IB23Y6Tpz4HMeO+VFbO13xOBMSo0ZVqQoLj0c6Cfh8XsWFPhwOifal1WrTnQ+U\nPhSSXGbIvsvDvY+FWm+YTFB23sy/UAgrU88mlHHddd/I4R4R2VBY6IDBYFTNsWDVPXrRJCyOHTum\n+LfBYEBZWRl+9rOfjVhhkaljEYvFwPO8eJFn3TsTp5HqhTkWZWXlokDx+31nZ4Ik32VKzsvACgv5\nlzfbRkN6aG9vF//es2c3Fi68eUjUtm/d+gxOnDiG55//vaJ0j4VCmLOS2LxGfhx9Pp+iYiQYlKpt\nbDYbYrGo2IlQC0wgqCX2MmEhd7/Yeof7rBC1braZoFYVkk+OBY0iH15wHAen06m46YtGowgEAhk1\nxwI0Covnn38+o5UPR7LNsUgcCMZ6WWTb1lsuLFjnOr/fj9LSMtWqEBYKGVzHYuAuRG1trQCE49PV\n1YmDBw/gkksuG7Dtp6KnpwexWAwej0dRFscuYkxYJCZzyuOh8udYbxJ2JywXwlocsXg8LuZsqAk/\nSaRKFxUpFDLcHYtcVYVEYDSawHGcrCokvxwLQL05FpGflJSUoKWlWfx3NqWmgM7kzVAohOPHj+Pz\nzz/PK4WdS7J1LBIv8qwZTLa9LFgPi7KyMjEpiiVwqlWFSHdKA3tCk+dYDKxjIQiLf//3hQCEcMhQ\ngH1G8tAGIF3EqqoEKzJReCaGQhjSSd+q+L/Wz1meJ6EWqpIci+SqkOEeClFrOpcJwlwQ4fcvhULy\n53xKo8iHH8XFTgSDQfF7mE07b0CjsIhEInjsscdw6aWX4pvf/CYWLFiASy+9FI8//nhW2dH5SLY5\nFuwunQkLpgizFxYsebNcFBbsgqNWFSJdcAa2MkPuWGRyMn3hha3YtOnXupdraxNyLGbPnoMJE87F\nP/6xL2dlvtnAPqNEYcFCIWVl5apN1BJDIQwpB4IJC33JxnJhEYlEkipO2HqUfSyYsBg5yZvZVoWw\n3+JgVWdlg/QdIGExXGD9qNh1JJt23oBGYfHEE0/g9ddfx6pVq7Bz507s2rULDz74IP73f/8X69at\ny2jD+UruHAtlKCTbJlldXZ1nY2UlogvCToRqVSGD5Vgocyz0n5zfe+8dvPfeO7qXa29vg91uh8NR\nhGuuqUM8HsO77+7RvZ5cwoZaAWrCQhASDocDRUXFSd8PVhUCKC940gwH4fNlFy6t31dWaspI/Iyk\nUJ7kWHAcB4PBMOxvMnJZFSKv2gHyTVhQjsVwY/LkWgAQz4kDEgp544038PDDD+P666/HOeecg3PO\nOQff/va38dBDD+H111/PaMP5itlshsFgyEGOhXCRZ8mbuXAsSkpKYTQaZaEQ39ltpq4KGegTmjLH\nQv+2e3q6EQwGdfX94HkebW2tGDWqChzH4aqr/gVGowm7d+/Kun9INvj9fnH7iRnZ7CJWWOhAYWFh\nkrCQh5TkoZBEx4Jl7mv9nBNLRhMvoGqdNwEhgZONWx+uqHWzzYRwOCI6loPVqC4bmHilGRzDh6uv\nvgZFRUV4883XEQwGZcKiHx2L3t5ejB+f3Jp1/PjxYtvPkQLHcbDZbP3gWGQuLHieR2dnp1gZIE/e\nBJTlbYzBulPKpo9FMBhEOBwW6+i14vX2IhgMiqVTRUXFuOKKWWhsPINjx47q2odcIm9ipuZYGI0m\nWCwWFBUVJTXCkgs0pWPBGlhlmmOR6FgkCgvmfimb5phMphEVCskm8TgajciqdvIxFCLcVGU6K4UY\nethsNsyfvwBerxdvvbVT1s67Hx2L8847T7UyZNu2bTj//PMz2nA+Y7PZM3YsEi/yuQiF+HxeRKNR\nlJcLA3+kclPhwsUuDsqW3paz+zNwJzSe5xXVDHqFhVzE6rnDY/kVLBESAK666l8BAAcPHtC1D7lE\n7rG1pYYAACAASURBVDTIBRd7zuFwgOM4OBxF4HlecWHr7u4WG9fIH2cXKGZT623oligOEj8jtT4W\ngOBYDOcGWYnHPzvHQsqx0JsDMxSQvmPkWAwn5s+/DhaLBf/7v38Sb3T6tdz07rvvxq233or6+npc\nfPHF4DgOBw8eRHt7OzZv3pzRhvMZm82WscPQH1UhHR0dACA6FoWFyuRNtaqQwehj4fX2Ih6PobS0\nDG53VwbCQhIlgUAQxcXahuOwUtNRo0aLj5WXC8dK7hoMNPJtJyaS+nw+UXSy/zOxIQg0D0aNGoW2\ntraEqhBly212V6k12bjvUEhyHwtAmHsxnIVFOBxGPB6DwWBAPB7POMeCNchjx89sNp/tjpt/jgUJ\ni+FFcbETX/taHf7859fFPLZ+Td689NJLsWPHDsybNw9+vx9erxfz5s3Djh07cMkll2S04XwmG8ci\nsY+FyWSCzWbLqkEWa9ksCQvhQiQ5FslVIYPhWLA8gsrKyrP7lbmw0ONYsK6bVVWSsBgKSXPymL08\nx4LneXi9XpmwYHk4gqvV29uDeDyOMWPGnV2PJFDYBY+9v2xzLBI/o8T1M4Z7KIT9PtnApkwTVRMb\n5HEcB4vFkmehEOG3R+Wmw48FC66HwWDIagAZkMaxWLx4MX71q1+huLgY27dvx/z587Fy5crM9naY\nYbfbzt7BxGEw6JvjpnaRdziKsmqQJTXHEkIhicmb7GKgPjZ9IIWFYK9VVo7C8ePHdMep5WEUPdax\n5FiMEh8brAZhclLlWASDQcTjMVFQJDZRY8ehoqISRqNJIUrZcWGxe70to5NDIZGEfyuTQxlGo0Ec\nBz4cYWGQkpKSjNw2hnpPmcxztgYDKjcdvlRVVWHu3P8H77//LjiOE29S9ZLyqvjRRx+J9unPfvaz\nrDtDDifYXWAmJwO1i7zD4cjKsZDmhAiOhd3OQiFSjoXRaFKIoMGoCmF35SyJUq9jIW9rrccxYjkW\n8r73rKphMO8U5TF7n88nik6pIkTIlUmsHGIipLS0FIWFhaplkEw46S03TazsSPyMgsEQTCZT0mAi\no9GU81DI/v37FN0ABxNJWAj1/pnmWKh1wbXZrAM+6TcbqNx0eHP99d8BIJx3MhlABqRxLCZNmoT1\n69fj8ssvB8/z+Mtf/iLeOSXyrW99K6ON5ytSfkJA9+hftROLw1GEhoZTiEajinkRWpG38wYEW9pi\nscjKTSMqMXETDAbjgJa5SaEQwTnQe1GXJ2/qyQ1pb29DUVGR4rNid1uDeUJnn4/D4YDb3Q2Px4PK\nykox5CEJC2UeDjuOQs+SwoTkTeXdpF4RzMRBqlyCSCSsWg1gNpuTemBkg9fbi0ceWY1Zs+YMiQmV\nTPgzYZFpVUhigzwgswm0gwk5FsObc8+diBtu+HfFd1QvKa9iDz74IB5++GG8/fbb4DgOa9euVX0d\nx3EjUFhk41gkl36yC4jP5xVjuHpg7bxZQqKwToeiQZY89MKwWi0DemFld9osJKE3Tq0MhWhzLHie\nR3t7GyZMmKh4nB3/wewfwEIh48ePPyss3KisrBQ/t8RQCBMc7DiUlAjN0FwuacCa1NJbmbypt6V3\nQUEBvF5v0vdDGHCWLCyMRmNOG2Sx8trOzo6crTMb5KEQIBeOhTIUkk85FtTSe/iT7fTnlMJi5syZ\nePXVVwEI5aa7d+9WXLhGMuwHlUkCp9qJRZpw6stIWHR2dsJsNiviYQUFBeIdfjgcUggZxkDHdhND\nIXpPpr29+oWF292FaDSqKDUFBEFsNpsHvKW5HOZYjB8/Hv/856ei8JKEhfB5spIvFo5kr2OORTQa\nRTgcViQBJg8h03asWY6FzWZXFRZsO4kI5aa5cyzYMUhsHDZYMBHIWh9nn2MhdywsYvt0rdaz3+/X\n7ZbmCio3JfpCU+bh22+/LSYGEtIPKhDIJsdC0nQs8zbTPBa3uwtlZWWKk1JBQYHY2VHe6U+OHsci\nFArhpZdeEMMuifj9/j5FCrsglpdXgOM43Xd9mSRvquVXMKxW66Amb7KLJ2s+x46P1lCI4FhIbheQ\nO8eCCZLkqpCQamzdZDLlNBTC7orllUCDSWIoJFN3Rn1uj75eFocOfYT/+I8bcejQRxntQ7YEgwFR\nmBOEGpqExdixYzNO4mBs2rQJN9xwA2bOnIkrrrgCt912G44fP654Dc/z2LhxI+bOnYtp06Zh0aJF\n+Pzzz/tc986dOzF//nxceOGFmD9/Pt566y3F88888wxmz56NWbNmYcuWLYrnDh8+jLq6Ol137vIc\nC72onVjYxSGTJlnCyG03yssrFI8XFBQiFhPuZOWzCeQIFqy2933w4Ed45ZWXsHnzU0nPRSIR3H33\nHXjggf837To8Hg/MZjPsdjssFv1hGHmOhda+DFJFiJqw0Pb+eZ7H+vW/wPvvv6ttRzXC7oLHjRPK\nRplgYBexxFCIzyd8P9jFVm0uTKJjoX8ImSAOmLBIzCUIhUKqYTWj0QSe5xGP56atN/ttBQKBITGD\nJDEUktuqEH0VSsePHwMA/PWv72e0D3I+++xT/P3vH+haJhQSxGW21wRi+KKvVjIL9u3bh+9973v4\nn//5H2zduhVGoxFLly5VWJ2bN2/Gli1b8POf/xx/+MMfUFZWhqVLl6ZtHnXw4EGsXLkSCxYswGuv\nvYYFCxbg9ttvx8cffwwAOHr0KJ588kmsXbsW69atwy9/+UscOyb8MGOxGO677z488MADujKcs8mx\nSOxjAUhWdyZNsjweD3ieR2mp0lGS38mmyrGwWKyawxHMtv/ww3qcPHlC8dxf/vIGmpub0NTUmHYd\n3d0elJSUiLX72TTI0rrfTFgkhkIAnA0d9L0PXV1deP/9d7Fnz26Ne6oNv98HjuMwduxYAEgKhbDP\nMLGJmtvthtFoQmFhYVKX1cSx5npFMAuFsMoi+cUuHo8jGo2KlSZyWNJxrkSAsnnY4LsW7Psv9bHI\nTFhEo2rJm6xyR9t3mrmGBw8eyHrWzW9/+xTWrn1cV0VPIBCgMAiRlgETFs888wxuuOEGTJkyBbW1\ntXj88cfR1dWFjz4S7Dye57Ft2zbceuutqKurw5QpU/DYY4/B5/PhjTfeSLnerVu34vLLL8fy5ctR\nU1OD5cuX47LLLsPWrVsBACdPnkRtbS1mzZqFWbNmoba2FidPnhSXnTJlCmbPnq3rveQmx0JZbgpk\nJiwSK0IYbF4IK2NMrAoBhDI3tdHYashF1IsvviD+7fX24ve//x8AyqFaifA8D4/HA6dTsJItFquu\nk3MsFlN0o9R67NvbhcRGeXMshtZQCLuoJM7zyBa/3w+73S6GGZnITgyFGAwGMZkSALq73aJASwyF\nJPaxYCJOe46F4Fiw+L1c/CWWssqRRqfnJhwSCEjCoqdn8PMs5HkvZrM5i6oQtXJTfb1GWHm5292F\nL788ndF+MFyudsRiUTQ3N2lehjkWBJGKARMWifh8PsTjcbFlaGNjI1wuF+bMmSO+xmaz4dJLL8XB\ngwdTrufQoUOKZQBg7ty54jK1tbVoaGhAc3Mzmpqa0NDQgClTpqCxsREvvPACfvrTn+re9+xyLJLv\nWLIJhbCTTGJiLbswsPBBKscC0Hb3L69dP3DgHzh69AgA4NVXfw+v1wuDwXh2noK6OPL5vIjFomLy\nm96Ts9fbC57nxZCG1gsl67rJSlzlWK1WTY4Fu6gkzvPIFp/Ph4KCQlEkJDsWUte7oiKhiRqbt8Lu\nnBNDIWoXfz0hLynHQvj+yB2IxHbhcoxGI4DkBluZIheyWhyLX//6STz33DM52bYa7PgWFBTCYrFk\nURWi1gVXX08ZeZ5TNrNuAoGA+L4aG89oXi4YDJCwINKiv2lCjnj44Ydx/vnnY8aMGQAAl8sFAKio\nUOYKlJeXi3edanR0dCQtU1FRIa6vpqYGK1euxNKlSwEAd955J2pqanDLLbdg5cqVOHDgADZs2ACe\n53HHHXfgmmuu6XPfq6vLYTYbYbEAlZX6Wp5aLBzMZiOqq8vEZceNGwWz2QizWf/6gBDMZiPOPXes\nYtnRo4V9ZM+XlhYlrbusrBhmsxFFRWaUlKTfrtkMmM1GLF26BL/97W+xffvLuOeee7Br158xdmw1\npk6dinfeeQc2G6fYDvs7EHDDbDZi7NgqVFYWobi4EB0dAc3v1+/vOvs+x+PMmQYYjXFNy3Z3d2L0\n6FEYOza5osnpdMBg4FFWViBeGNU4dUp478Ggr8/X6iEaDaGqqgpGoxEVFWUIBLyorCwCz0dgNhsx\ncWK1KDorKspw+vRpOBwm8HwMY8aMQmVlEcaOrYTZbITJJBwPgyEOi8WEsWPLxRi40+kAz8c0HS+H\nwwKz2YhRo0rPfselz5PnAzCbjSgrK05al9NZCLPZiJISO8rKMmsDLMdk4s9+fwEgrPqdYni9Xrz3\n3m4UFBTgrrtu75fYP89HYLNZMG5cBRyOAhgMfAa/VaCgwASz2YjKSqe4fGVlCcxmIwoKjJrW2dvr\nQUVFGbq7u3H06CeorPy+6uv6WteZMx7xGHd3uzRtm+d5xGIRlJYmfwfyleHyPoYSmoXFhx9+iD//\n+c9obm5OiqNu27ZN10YfffRRHDhwAC+99FLSSToXJ4XEsq2FCxdi4cKF4r9fe+01AMDs2bNRV1eH\nl19+GfF4HAsXLsTOnTv7LKsNBOKIRGJob3fD5dLnMng8XkQiMfT0hGAyCcv6fFFEIjG4XPrXd/p0\nMyKRGHjerFg2FjMiEomhoUF4PhLhk9YdjQKRSAxNTZ2IRNJfLNvb3YhEYvjKVy7A1KnTsXfvP3DX\nXT+F3x/EsmXfwxdffI5IJIYvv2yFySTcRVdWFonb/OKLRkQiMZhMdrhcvYjHDejt9Wl+vydPNiES\niaGwsASRSAydnd19LhuLxdDU1ILJk6eovjYeNyASiaGxsSNt6V5TkwuRiGDxnzhxJinslAmC89CL\n6mohcbOgoAhtbe1wuXrR3t6JaDQOny8Gv1/Yb6PRCq/XjyNHTiISicFsLoDL1YtIhEMkEkNzswsu\nVy/c7l5wnBEdHXLnyIjubm3frc7OXkQiMcRiwrHp6uoRl2tq6jj7XULSukKhGCKRGFpbPYjFsq8W\naG3tFI/5mTOt4vbk3ynGoUMfIRKJobu7F599dkI17JUtHR1umM1WdHR4wfMcenv9un+rAOByeRCJ\nxOD3R8Xlw2H+7LHr6nOdkUgELlcnLrxwGoqLS7F//0F8+WW7mGzLUDtOiRw/3iAe488+O6bp/YRC\nIYTDUcTjhoze/1BDy3EiBPQIME2hkD/+8Y9YtmwZfD4f9u3bh7KyMvT09ODw4cP4yle+omvnHnnk\nEfz5z3/G1q1bxTI7YaeFwVTMaWB0dnYmORJyKioqxOmeWpZxu93YsGEDVq1ahUOHDmHChAmoqanB\n5MmTMWHCBDHpMx3ZVYWknjSaSU8FeYWAHHahZPa6elWI9lJEKXZvx/e+twgAcOrUSUycOAlXXfWv\nSZZ8Imx6J9tPi8WsOb8DkN5nZWUlOI7TtM8dHS7E4/GUFxqtg9hSDQvLhkAgAJ7nxVwYp7MEfr8f\n4XAYXq8XhYWFCnHMcktYgiyrTkgOhYSSOiIKQ/MyKzeVh6ukOSHqVSFA/4RC+jrmx44dFf8+depU\nTrafCAtbAUIYI/OqkOTkbT2hEBYGKS8vx4wZX0UsFsWnn/4zo32Rnze1hkKonTehBU3CYsuWLbj/\n/vuxbt06mEwm/OQnP8H27dvxjW98Q1eTloceeghvvPEGtm7dipqaGsVz48aNQ2VlJerr68XHQqEQ\n9u/fL4ZL1Lj44osVywBAfX19ymXWrFmDRYsWYdy4ceB5XpENHYlENJXLsZNudjkWyZNGM+kCKbV3\nVo4QZydB9ny6HAstCYzyE8rkyVNw+eVXAACWLPkBOI5LmmeRCMtPkHIshP3RWkXAckWczhJYrVZN\nF0q1qaZytA5ik4ulXCVwSjF74ffDhILH44HP5xNDIAzW64RdACRhkdjHIph04bfZbIhGo5q+2/IG\nWYCy+oEJX7VWzsx5zNW8EHnyZl85Fqz8EgBOn+4vYeEVRVw2ORZqVSFSMrgWsSyIgfLyCsyY8VUA\nmedZdHRIN3FNTY2avh8stynRISEIOZqExZkzZzBr1iwAwo+KnRT/4z/+A3/60580bWjVqlX44x//\niLVr16K4uBgulwsul0tcF8dxWLx4MZ5++mns2rULx48fx7333ouCggJcd9114nqWLFmiaC++ePFi\nfPjhh9i0aRO++OILbNq0CXv37sWSJcktSevr63HixAksXrwYAHDRRRfh1KlT2LNnD3bv3o1Tp07h\noosu6vO95MKxUJs0msldELuTLy5WCovCQuGCxZwC9aoQ9j60CAvJsQCAFSvuxJo1azF9+oyz20uf\ngJrsWDC3QNt7ZssXFxfDZrNr6mORrtQU0D6ILNUU0mxgLgg7bqzxUne3B15vb9JUQSbcmLBgx1Fe\n/QMIF/9kx0L7hUve0htIrAoRjpNaYyTW8C1XwkJ+zNM1yeJ5HsePHxWPY0ND7oUF62zKjkmuq0Iy\ncSzKyspRW3se7HY7PvooM2HBEr8nTapBNBoVfy/pYOc8tXkxBMHQlGNRUlIinriqqqrw+eef47zz\nzoPH49Fssb744osAgO9///uKx3/84x9jxYoVAIBly5YhFAph9erV6O7uxvTp07FlyxbF8LMzZ86g\nurpa/PfMmTPF/hQbN27E+PHjsX79ekyfPl2xnWAwiFWrVmH9+vXi3VVVVRVWrVqFBx54ADzPY/Xq\n1SkvQnKy7WOROGmUXWQzWZ/H44HD4UgaXsZOtMwpUHcs2Hb7vkgnWqCFhYWorT1Ptr30oRDmnDDH\nQhmG6Hs0L5tsWlxcrNmxSNd1U9gH5tikFzf9EQphF04mDJgD4XK1IxwOqwgL4d+NjYmhEGUfi1Ao\nCIulUrGs1Ceh76F5rFxUvSpEOE5qNjgLheSq+yb7vhmNJlFUqtHc3ASv14srr7wKhw59hNOnG3Ky\nfTnMDWLH2mKxIBaL6mrBzUjXeVOLc8hmp5SXV8BkMmHatIuxd+/f0dLSjOrqMbr2ha1r+vQZOHny\ni7Pn1vTroHbehBY0CYtLLrkEH3zwAWpra3HttdfioYceQn19Pf7+978nlXqmgjWlSgfHcVixYoUo\nNNTYs2dP0mPz5v1f9s48TIryavt37z0rzDAzbDPszCAwwICK7MgiBEIUIglE4Q36CviJGkU0fggK\nUUCNWzBuJCbmE41rcH95VTSKIyAGFET2dWSZfe3u6a2+P4qntq6qrp7unp7l/K7L65Jen67uqefU\nOfe5z3RMnz5d97WdTie2bt0acvvs2bMxe/bssGtTvhYQfkNWm1aqNWnUYrE2yV66trZWdb4I25hq\narQ1FuwxRq7+3W4P7Ha7LCCSEs6LQytjEWkpJD29I5KSksJaPR88+CO++upLANqBhahtMZ6xiFXL\nKQtWxFIIH3CxjIRykjD799mzfGDBjqPD4YDZbEFDQ/1F+3ZviIGV0ZIPIA0smMYiNGOhNYQMAHy+\nWJVC+JbG5OQU3e+a6SsKCi5BVVUVfvhhHzweT0w1AOz7Z38vLCjwetUnveqh5rwZyWh7ZXv58OEj\nsHPn1/jPf77FzJmRBxZOpxP5+fwFQknJaVx++Ujd55DGgjCCoVLIqlWrMHPmTADAkiVLcOONN6Kq\nqkoIMtobJpMp7FXzvn3fY+7cq2XCMoA/sVit6nM7Ih3KFQwGUVdXG6KvAKTiTVYKUQss5Gl0Pfje\nde2rFGWtX4nULVK6HqOlEDGwSL/oP9GoKvwsLy/HE088invvvQvnzp3FVVf9TDOwYOnocNqW+Gos\n+OPBMjlMnKlVCmG/OZaxYCZZzAiN47iQjZ/V8I0EkKyUYbPZQoJdcSR76G+JBdCxK4U0ICkpGR07\ndtTVWBw+zAKLAejVqxc4jovaNEqJ0gmVXRg0RWehVgqNpBQiZiz4wKKo6FIATdNZlJeXISsrGz16\n9AAAnDlzOuxzSGNBGMFwKYRhNpuxePHiuC2otRCuzn/0KD8H5cSJ47KSgf7cjkinfdaC47gQfQUQ\nmspWK4WECwakeDwe3THJ0gmtatTUVCEjI0NIHYviTaOBRQ2cTifsdjucziQEg8GL2R/xc505cxp3\n3XU7vF4v+vTphxtvXIyBAwdpvqZRbYv0+MSyKwQQvwOWgfjpJ94BMTRjIbZ6mUwm2XfOAguxa6Pp\nGQsWGFitVqFzhyF2NGg7b8aqFOJ2e5Camoq0tHR4PMfQ2Niomh04fPgQbDYbevXqjVOnegMATp48\njvz8gpisAwjVw0gzFpHCMjrqXWHhMxaVlRUwmy1Chis7Oxu5uXnYt+871QypFo2Njaivr0ffvv3R\nuXMXWCxWocymh6ixoIwFoU3CnDdbO06n/shxdoWt3LS1Jo1KR14bRTrlUgm/MYR2nkgJp4uQYjRj\noVYKEe28xXWKGQtjpZCamhrBpVXrRPzdd3vh9Xoxd+48/PGPT+oGFUBk4k2n04m0tLSYizfZlZ+Y\nseBLIcquEGmgkZaWLitJpaSkoqGhXriaDA0sjLcVs64Qi8US0lYpOm9ql0Ji2RXCMhaAfAAdw+Px\n4OTJE+jbtx+sVit69WKBRWwFnGLGQl4KacpcFDFjETqEzIiIuqKiApmZmbLvv1ev3vB6vRFNgpVq\nNSwWC7p3746SktNh27+pFEIYgQKLJpKUlKR7ohYDC/mmrZWxcDqdEWsstDwsGNJ0ulowIwr/9AML\njuPgduvXrR0OBywWq2r2g02olAZARj0k2PvX1tYgPZ1/vla7L+tIGTy40JCoTkxB62+4Lhez3s6I\nWykkPb0DTCaTEKxqlUKA0EAyJSXlov8F//mj6wrhMw4sMJW3m2r7WIhDyKIPLPx+P3w+H5KSkoTM\njNq8kCNHDoPjOBQUXAIAyM3tAZPJFLGA8+uvv8KJE8c172e/aVZeZKWQpmQsRI1F6BCycH8LwWAQ\nlZWVIQZ+kU6wBcTAgvn95ObmwePxhHgCKWHvQRkLQg8KLJoIy1hoRfhs01cGFlqTRnnNRtMyFlqB\nhbQDIBqNBe+BENDNWLBav1rGgm3G6hmL8Cdnt9sNv98fkrFQimelg6KMwF4nXNbE5XIhOTkZHTp0\nRH19fUwmeCrT62azWZhyC2iLN4HwZmhqPhZAZO2mfMbCJjNtY9+Vuo9F7Eoh7HtNTk4SvnO1EpRU\nX8Gvy4Fu3brj5MkTho3XXC4XHn10Pf72t7/oPgZQy1g0pRSi3RUSLnNWXV2FYDAQ4vwaifiTIfph\n8K+Vl8frLEpK9HUW7D30yqIEQYFFE5HW+dVggYU0G8BxHHw+n9DzL8VudyAQ8Ec0HZKJ2tTEm4A8\nsFALZpQeCFoYTX9qBRZKcyzpeowEFtJWU0D7RCy2BRoLLIwYk3EcB5fLhZSUFGH9kegs6uvrsX79\nWnz//V7Z7cp2U0B+fJSBBcsIAWoZC/6xzONAufFHorFggYHVaoPDIZ9AK3aFhGa/YinedLn431u4\nUggLLFhXA8CXBVwuV4iDrxaVlRXgOA4XLpzTfIzSzCzSMp4Uta4QsRSiHxhUVlYC4MsXUljAH0kp\nVVoKAcTAIpyAU+lnQxBqGAosPvnkk5iNQ24rhGs5ZZu+dNMOBALgOE51kzfa+iglXClEummppa+l\nrYp6sJJDOCV4amoqGhoaQq4Wla2mQGTpZLEjhA+gtI49C2qU+gQtjIg3PR4PgsGgUAoBoOuroOR/\n/ucD7Nq1E59//pnsdjGwEIM/9vqAvPQB8Bkh5r6p/L7Z52Ubj1JjIW48xjMWVqvlohGUMedNqzV2\nGgvmusmXQvjPqjzmHMfh0KFD6NQpS1YaiFRnUVXFH7Py8nLNc5zSx4KVFZvaFWIymWQzkqxWK8xm\nS9hSiDLLwIhEQ8NQBha5ufx4hXACTjLIIoxgKLC46667MH78eDz66KM4fly7FtmeCGfrLZZCxE2b\nZTfUyhJNsfXWsvNmSDdYtWBG2qqoh/GMRSoCAX/IRq0mMmX6BiMnZ9FdVF4KUR77hob6i58psoyF\n3pWimAYXMxZsMwqHz+fDBx+8B4A3vlKuFZAHFtKMhVpwxLIYahoLQJqxUAYW/L8jaTe1WCyw2+3w\n+/1CoKjvYxG7WSFsnUlJycJvW9lyWlpaipqaalnHFQD07NkLgHFrb+YLEQwGhf9XohRvRtoqLYWJ\nt5UaIKczvOmbMhgQn9sUjQX/WZnGolu37jCZTDhzRr9Vl9pNCSMYCiy2b9+OW2+9Fd988w1mzpyJ\n+fPn46233pIZB7U39DIWfr9fODlKN221HnZGU2y9maBNuxQibk5qwQwAg4GFsfQn2/iUGRB2tSm9\nIhcDqfCfV1nyEZ1PQzUWSUlJht0QjYjmRCMrMWNhVMC5ffsXwmPLyi4oXteFpKQkmbpfmomILLBg\npRCWsWh6KYRdtVss1hBnUiPiTSb+jAZpxkIrsDh06EcACAksevXqAyDyjAUgzpZRIgYWzNI7uq4Q\nrb//cN+P1M5b/tzINRYVFeVwOBwS3YgNXbp0RUnJGV19CnWFEEYwFFikpqZi3rx5eP311/Hee+9h\n6NChePzxxzF27Fjcd9992Lt3b/gXaWPo2XpL276kwZc4gEzdIEvr9bSorq6G2WwOSZsz5BoL9VHW\nrFVRD6MnEy33TbbhyTUWxtPJTGORlha+FGJUuAlIU8jaa5DW16WDwsLBcRzeffdfMJlMyMrKRnl5\nheyEzTpNpEgDBrWsCxN3apdC+I1HGURG4pOg9LEAxO9I1AfEt91UmrEQu0LkgYWavgLgr8BTUlIM\nBxbsmAF6gQXLLjXN3E2Knng7XGCh7ORgNEVjUVZWhk6dsmRBeF5eHurr63VLfWTpTRghYvFmv379\n8Nvf/ha/+tWv4PP58OGHH+K6667D3LlzcfDgwfAv0EbQy1hIhWbyUkhoDzujKRkL3tuhg+YV+uWR\nugAAIABJREFUeriuEPYYr9eruyGIYjr9kwnbDJWBBbtqz8jIFG4TswVNyVhoize1giw1jJSfpN0b\nkWQs9u//HidPnsCoUWOQn1+AQMAvuzpmnSZS2Os7HA5VoyPlwDLl7UwkqwwAtUpHakgDC6XAVsuA\ni388H4TEphTC9CdJSEpKgtVqDclYHD9+DCaTCb1795HdbjKZ0LNnL5w7d1b4fTCrczVY0AtoBxbK\n7FJ0GotQS3+ABRbhSiFaGQvjgSPAf591dbUhJZW8vJ4A+HlMWng8bphMJs3zCUEAEQQWLIi48cYb\nMXnyZOzYsQNr1qxBcXExtm3bhl69euGOO+6I51pbFHoaC+nVldfrFVKmosZC/cQCRJaxqKmp1iyD\nAEofC+1SCKDvvhlJV4jaa1VVVcFms6l2qRhJJ7NNJVRjIQZ1fr8fHo8nJAugBzsh661B2r0haizC\nBxbvvMNP/b366jnIzs4BwOsCALHTJDSw4DMRWsHRhAlXYvTosYKOgKEshShP+k01yBJ1MPzx8Xga\nYbVaVQPZWIo3pV0hJpMJHTtmyHwsOI7DyZMn0L17rmqQ06tXb8Hae8eOYtx11+8wf/4vVa2+5RmL\n0pD7AfnIdCD6rhDtjIV+oFJRUY709A4h2cdINDSA+JmVmY/u3XMBiPNq1PB4PHA4HBEPXyPaF4b8\nX//whz/g/fffh8lkwtVXX417770X/fr1E+53Op244447MGnSpLgttKWhl7FQXl25XA3o0KFjmIyF\nMZMchtfrhdvt1uwIAZQZC+1SCMCn/LVeK1KNhTJjUVVVKbPzBoy7XgKh7aZqqV+lct8IxsSbYimE\nZYfCdYWUlJzBt99+g4KCAcjPL8CRI7y9e1lZKQYMuEToNFGWO1gmQqucM2zYcAwbNjzkdvY9s1ZR\nLY2FkaA1EAjAbLZcvCqVd+74fF7N4DK2pRBRYwHw37t0s7tw4TzcbndItoLBAq81a+6T6YeOHDmE\nHj16yh5bVVWJtLR01NXVhuhgGA0NDUJwCETnY+H3+1Sv9h0OJwIBv6YtN8dxqKgoF7o3lM8FjJdC\nWHdJVpZ8Cq44M0RbwOl2u8kciwiLoYzF0aNHsXr1anzxxRchQQUjJycH//jHP2K+wJaKvsaC3wjZ\niZGd3MRZC2pdIcYHEQHhPSwAuXgzfMZCW8ApZiyMlUKkr8XsvJXp+0hOzrW1NTCbzcLrqwV1ojmW\n8VKIkTY/qUOm2WxGenqHsBmL9957BwCfrQAgbErl5by3glqrKSBqUCIJjvjHh3peSIlMYxEQsg/K\n78jj8Wj+jsSukFiIN8WMBcBrSrxer/C3xlwytQKLfv3yhdeZOHESliy5BQBw4YI8cOA36wp07twF\nGRmZqqUQ3nXWLftOonXeVAscwrWbNzTUw+v1hpRB5M81lu3U6i7Jze0Bh8OBHTu+1vxsjY2NJNwk\nwmIosFi2bBmmTZsWsiH6/X588803APiT9OWXXx77FbZQ9DUW/KbftSs/xphtTnpdIczJzmhgUVen\n72EBiCp2QL8rBNC39TbqtqfWFVJXV4tgMCDTV0jXYySdXFtbi7S0dCHjwQI2qVOpcgKlURwOu+4G\nIW03BfhyRTiNxY4dxcjIyMTIkaMA8IOiALGGL+00kZKe3gGjR4/FmDHjI/oMys+sDCzMZjNsNpsh\nZ9dAwC9kH5SdO3pjwtlvOjaBhTxjoewMCRdY9OnTF2vWPIRnntmE229fjqIiPsujDBwaGurh9/uR\nmZmBnJwcVS8Ll8sFjuNUg/RIu0I4joPf729Su7lyXLoU8VxkNGNRpvpaDocD06fPRFVVJT799GPV\n5/IzgyiwIPQxFFgsXLhQdXRxXV0dFi5cGPNFtQaMdIV06dIVgLjR6vtYRJaxCOdhAYgbjtKQR/6Y\n8IPI2BVk+IxF6CAyNddNQNyIjJR+amtrZJ9T1KOIQR2bkxFJVwj/WvrD5KSlEIAvV7jdbs3vieO4\ni6nzbEHsxzIWzA1S6eTIMJlMWLHiXsyY8fOIPoOyxVZt83c6nYa7QtgVtVKk6PWqTxgF4tcVAojd\nMOzvKlxgAQBDhgxD585dAPApf7PZjAsXzsseIxVD5uR0VvWyUAtYm9oVojdpOFw5g2UZ1DIWan8P\nemhlLADg6qtnw2az4e233wj5LjmOg8dDGQsiPIYCC47jVMU61dXV7dYoRRRvaneFhGYsjJxYjKUz\njZRCpD3q4TpH9MWbRp03Q0ens04IZSnEqEGW3+9HQ0ODoK8A1IO6ppRCAOMZC3bFKtp6q2ctvF4v\nAgG/7Ao3NTUVSUlJgkmWck5ItDCjM4ZWYGF0Vggrayg30MbGRs3MlxhYRD9HRQws+O+ZiVqZtuXE\niePIyMjUzdYp19apU6eQUgj7bWZkZCInpzOA0KyG2nfV1K4QtQFkjHDzPrQEl4B+UFJXV4vly2/D\nzp07hNu02lYB/lhcddV0lJeX4fPPP5XdZ2RmEEEAYcSbS5cuBcCupFbIUvjBYBBHjhxBUVFRfFfY\nQtFzuxNLIXzGgp2c2IklFj4Wok12huZjlLMN1DCSsTCusWB6jTrhNq2MhVGDLFG4GS5jEbl4k1+H\nAw0N2k6aSnMkFiBVVVUJV8RSxFZJeTYiJ6czSksvCB0h/GNiE1jw6xPntKiJ6xwOpyEr8kBAmrEQ\nA4tgMAi/36+ZsWDPiWcppLa2BjU1NaioKMfw4ZdG9JqdO3fB/v37Ls7q4f/+2GbdqVMnYd18YFEo\nPE85hRZoeleInnibCSnPnv1JNRPDBJeRaiyOHz+G48ePYdOmZ1FUNBx2ux3l5RWw2+2aQfjs2XPx\nP//zEd588zVceeUUIWgkcyzCKLoZi4yMDGRkZIDjOKSnpwv/zsjIQJcuXTBv3jw8+uijzbXWFoWW\n+yPAZyxSU1MFQycjGotIfSyMZCxYKllLcAdEKt7UP6Gwk6+0FMKu7Dt2lGssjF71KVtNAT7Q5afB\niidSVgqJXGPhDJOxkG8s4QaRaQUNWVnZcLvdaGhoCCmvxAKpgFM9Y5FkeGw620hYsOv1enXNsYDY\nOm+6XG7Y7XZhHSyorKmpwbFjxwDol0HUyMnhg0Cptbpo3KadsVArhTS1K4SNlFcL9JnR16FD6l5A\nWgPIAH0NDcv+VFSU43/+5wMAvMZCaY4lpVOnTpgyZSouXLiAL7/8t3A72XkTRtHNWKxfvx4A0L17\nd9xwww0xPRG2dsK1m6alpYds2vpdIZHNChFtsrXTwbx7ol2z1RQw5mPBvDrCBRZmsxnJycmKUoh6\nxsJkMl0ccqV/1aeWseDXkhTTUohWuc/lcsHpdAp6iXAmWSywUJ58mYCzrKxU9So4Wthr8Z0uodcL\nTqcDPp8PwWBQ9X5GIBAIyVj4fF7hd6ldConlrBCXEBQDokC5pqYGR48eBdCUwIJ5iVxAt27dAcgt\nstnnUnpZqM10aWpXCAtEmJmYlH79+sNsNguOokr0dBEALgbaoeciaan2zTdfw8SJk1BbWxPSdqtk\nzpxf4eOP/xdvvvkaxo+fCLPZTAPICMMY7gqhoEKOlpshx3Goq6tFenp6yKatlwoV05mRZSyUG66S\nfv36CxMf1WBXunpzXzweN6xWq2qbnBI24ZQhZixCSzZ2uz3sVZ9ysilDObSpqV0hynkYShoa6mUB\ngGjrrRVYqK+DXRGXlZWFdJrEAvZaWsEf25yVw9CUSEsh0pQ/CwC1Xj+WY9M9Ho8sMJOWQpoeWPDH\nX6qzYFmAzMxMicBWK2MRajYXaVeInsbC4XCgV6/eOHbsqOoxrKgoR1JSkuZ52OlMUhVCs8Cid+8+\nqKurw9/+9hcA6voKKTk5OZg4cRJ++qkEO3YUA6CR6YRxNHeKWbNm4eWXX0aHDh0wa9Ys3Rd57733\nYr6wlg7baEMHYdUjGAwiPb1DyKYtaixCD7vYFWJcvGm328NmEf7whw26LnnGSiEew+nPlJRUnD9/\nTvi3VsYC4D9zuC4YMbBIl93udCahrk7cJFnwFmlXiLh5qnc8uFwuWVBkNGOh3ABE980LcS2FaJUq\n8vML8NVXX+LQoYOq2hAGL95kPhZi5w77XWqV1WLrvNkg+71ISyE//VQNh8MhCKONolbqqKysgMVi\nFVqZ1bws1IzX4tEVAgD9++fj+PFjOHnyBPr16y+7r6KiXDNbAfCBSV1dXcjtTK/yy1/+Ci+88Cw+\n/3wbAO3Mh5TZs3+Jbds+xkcffYDRo8eSxoIwjGZgIfWtmDZtWrMtqDWRlBRat5ZeYSs3bb0TC1OF\nG3XeZHbe4ax19dLegNiqGM7S2+jJJCUlFW63WxDDVVdXIS0tTTXbYbfbQq76vF4vXnvtFeEkyVoL\nlVoSvsuhUShhiOLNyAILqQdAmqKKwoSWzOoYMJ6x0AosysvL4ibeBLTT1KyGf/jwQYwfP1HzdeQa\nCzGbozcnBIhdKYTjODQ2NsoCWafTeVF0WIYLF86iV6++EVtKs2BK2nJaVVWFzEzRETYnJwdHjhxG\nICAeAzG7JP6u2G+56V0h6oFFfv4AbN36EQ4dOigLLBobG1FfX48+fUKNCRkOh1M1G8UyFhkZmZg7\ndx7++tfnARgLLHJz8zB48BDs3/89SkrOSDIWFFgQ+mgGFsuWLVP9f0KE39zkGQsWWHTo0CFk09bz\nsRBtl8MHFhzHoaamGj169Ipm+QDEVsVwGQu1UoYa8vJPR1RVVaoq2QE+wHK55P4o+/d/j7fffkN2\nm9lsQdeu3WW3OZ1JCAYD8Pv9sNlsqK+vh91u15ziqoVYCgk97mrW22lp6TCbLZrum2zOhTJokGos\n2O9AamAWLeECi759+8FiseoOCuQ4TrUrxOfzCSW6cF0h0Yo3lR4WAP8bTU/vgNOnT8Fms0RcBgF4\nQaLFYhVKIRzHobKyEv37ixt4Tk5nHDp0EBUVFYIm49SpkwDkA/SM6oOUsFZcrd8oGwF/5MghAGKW\n+OjRIwDELjM1nE6HqlZI2mEzbdrP8O67bwuTTY0wffoM7N//PbZu/Qj5+QUA1LuOCEKKoVkhhDrJ\nySm4cOG87I9Z2sVgMplkYka9rhA23MlIxsLtdsPn8+l2hERCuMDC7XYLZl/hX0tsX/V6vWhoaNC8\n0rLb7SGflwVm8+Zdh7FjeQfK1NTUEM8CaYudzWYLGRRlFL2ZJWplDX4oVkfN1k01sR/Ab0wWixWl\npaXCe8Y2Y8F/dj1nzD59+uDYsWNobFQv+wSDQQCQ+FiIIkX2PWldbcdKY6Elfu3QoaPgGNmUwMJk\nMiE7O1soddTW1oQ4wkrLJTk5Oaipqca+fd+hX7/8EE2CEX2QEj3xNgB069YdKSkpIZ0h27fznRlX\nXDFa87Wl83OkGQUWqCUnJ8Nms2HJklvw2muv4JJLLjG05pEjR6Fjxwx89tknQtaHMhZEOHQ1FkZp\njxoLgDfAOnXqJCorKwV7XGa1zerCKSkpEo2F9hULa6E04rzJfDKMGgSFIyUlFefOnVW9z+/nByMZ\nFWxJB5Gxq/rMzEzVx9psoaUQVtLIzc2TlSCUSMWzqalpaGioD7ENN4Jem6+W9XbHjh1RUnJGtZNE\nPJHLn2MymZCVlYWyslJkZmbKOk1iActYaGksAKCg4BIcOXIYx44dxcCBg0Lul45Ml74W3xWin7Fg\npYNoSyHiFbY8MJMG0b17923Sa3fu3AXffbcHHo9H1SJb2jkCFOLrr4sRDAYxblyoxbrNpm+spoae\neBvgfyP9+xdg797/oK6Ot7EPBAIoLv4K6ekdUFg4VPO1pRNspRs/O/ew20aMuAwjRlxmeM1WqxVT\nplyFN998Ddu28Tbf1G5KhENXY0Ho06NHT+zYUYwzZ04JJyil74JUzMhOLFpXLEbEjIAxO+9ISE5O\nFnQRSutvo3NCGNJSCDt5a5VR7HaHYLzENjOjU0ql7b7MRltt8mM49Np8tay3O3bMwPHjx+B2u0Pu\n07riBnidxf79319sy41dtgIQMxZ6V5MDBlyC999/B4cO/agaWDBdjHpXCMtYqAcWJpMJZrMl6oyF\nlssr+3symUxhWyW1EDtzSmWum8r7WVaDZQpGjx4X8lpq+qBw6HWFMPLz+cDi8OFDGDHiMuzb9x1q\na2swffoMTVt+QG7YJz0taAW6kXDVVT/DW2+9LuidKGNBhMOQxoJQJy+PjRk+I4yzVraBpqSkCJu2\nKN5UP7E4ncYCC/Yeeh4WkcA2cbfbFeIDEWmLmdTWu7KSPxGqdYQAcnU928xYxiKcH4V0FLjbzQcX\nkXpY8K/DrvS0MxbKIEfaGRIaWGh3fLCNq6qqsklBkB5GXFbDmTCxbIOyK0TqY8HKOGpYrRYEAsEI\nVy6HHT+1UgjAj/Zuqo8Cy0hcuHA+TGBRioqKChw48AMGDhyk2ppps9lVuzD0CJexACDoGFhg8eWX\nXwAAxo6doPvaohutPEB2u12wWKwRa4+kZGdnY8SIy7B79y4A1G5KhCd2udh2CNsczpw5LdymNHRi\nJ3y322UwYxG+3bSmpkr2HtGSnKxt623UzpshHUTGfAK0MxahDoZG20bFCaduSTASucZCT7yp1b3B\nAiU1AadexwcTcAKx9bCQvp6esC4rKwsZGZk4dOggOI4LuZ9lG5TTTb3eRqGMp/f6Fosl6lkhyjkh\nDJad69dPuzMiHFIvC6mHBUPqZVFc/CU4jtPc0OOhsQDEwOLQoYPw+XzYubMYmZmdVDNMUqQaCylu\nt9twtlGP6dNnCP9PBllEOMjHIgq6d8+F2WzGmTOnhNuUvgtyMaN+H7vD4TSoseDfI9YZC7WW00hb\nzKSj0/1+fpPV0liozVwwGiRIr9CaauctfR21gE4r+6DnZeFyNcBsNquefKWBRaxLIbm5eRgx4jJc\nccUozceYTCYUFAzAjh3FKC0tRefOnWX3s46O0FkhvrA+Fux50ZZCpGJDKeyYRxNYMPFhaekF4Xct\n7Viy2WyCl8WXX/4bJpMJo0ePUX2tpnSF6Im3GWlp6ejatRuOHj2M//znWzQ0NGDSpKlh22u1fseR\neNDoUVQ0AtnZ2SgrK6NSCBEW8rGIApvNhi5dusqEfLW1tbDZbMIfn3TTDndiCWcvzRAHkMWuK4Rf\nY2jGQusKUvu1RPFmfT1/4tXTWADqGYtwG690wqmaO6JR9EohWtbb4rTNmpDnuFwuJCcnq35/7IqZ\nf83YOtnabDbcd98DYR83YMAl2LGjGIcPHwwJLMRSiFxjwZdC+ICX+a2oYbFYox5CptZuCgCjR49F\naekFzJo1Cy5X08ot7PNeuHBe6IBRBr05OTk4fPgQSktLMXRokaZA2m63IxDwh/1blaI3hFBKQcEA\nfP75Nrz++qsAgHHj9MsggLYTsNvtEgacRYPZbMaNNy5FcfGXugZrBAGQj0XU5OX1wM6dX6O6ugoZ\nGZmora1GerpoXCXNWPh8Plgs6rMcAHmHgl66UdRxxDpjoVcKiUy8WV9fD6+Xfz1tjQV/gpVmaRoa\nGpCcnBy2Y0Iq3mxo4F+naaUQMd2vRMt6O+2ikxYre0lRE3QyWKodiH3GwigFBXyb4aFDP4ZsWMqu\nEJPJBIvFisbGxrBDyNjzou0KYVki5e/N4XDg17/+zcUuq8i0DYwOHTrCbrdfNJLivSiUwSjzsgCg\n2g3CkE5+NVoaCOe8yejfvwCff74Nx48fRefOnUNcONUQR6eLgQUzeItVhmHkyCswcuQVMXktom0T\nkcbi9OnT+Oyzz/DZZ5/h9OnT4Z/QDhAFnPzxqKmpkWUS2CbDAgs9RbjRQWSx7goxVgqJrN20oYHX\nWFgsVs1MgtrMhfr6ekMBgqixaDTcSaKG6IehFliol0L0AouGhvqQq22G1JQoUbN3+vTpC4vFikOH\nDoXcJwYWYveBw2GHz+cL62MB8BoLNsGzqbDfWzwCL5PJJIyv543bMkOyDSyrZLFYMXKkdlmJ/R1H\norMw0hUCAAUFBcL/jx07wVBGRG10Ost+av0eCSJeGDLIqqqqwsqVK7Ft2zbhSpLjOEycOBHr1q3T\nvCJtD7DA4vTp0ygouASNjY1ISxPnWrDNzuVquNj9oH1SYZtluEFktbU1guFNLDAm3jRu6c1eq7Ky\nEhkZGZonRjGQEjf1+vo6Xf8KhrzdNHjxvSPvChFntBgXb6alsaFY8sCC4zh4PB7NAIfV8KuqKhMW\nWNjtdvTu3QfHj4caZQWDfBmDlUIA0a8hnI8FwGcspNM0m4LUKTIe5OR0RknJGQDAJZcMVLmfzyoN\nHz5Ct8tImrEwipGuEADo2bO34PHCTOLCIbWmZ8T7WBKEFoYyFvfddx9Onz6NzZs34/vvv8f333+P\nl19+GSUlJVi1alW819iiYYFFSclp1YFZ8lKIV/eKz+ggsurq6piZY/Fr1CuFRJaxYLbarCtEzwpc\n2s4I8FfMjY2Nhq5WxdRvY5RdIdqlEFG7oZWxkKfkWdur3hUiE3AmqhQCAAMGDEAwGMCxY0dltyvF\nmwB/dS133ox3KSTegYVYjlIzVCssHIqcnBzMmnW17us0ZcIpy+bonQMA/jheeeUUXH75SPTs2cvQ\na4tiZjGw09KrEES8MZSx2L59O/7+97+jqKhIuG3EiBFYu3YtFi1aFLfFtQa6d8+FyWTCmTOnBddN\naYlCuml7vT7dKz5x6JN2Zwgby643NyBS9Eoh4snJeJ02NTUNFy6cg9/v181mSYdcSd/fSIAgzVgw\nIV50XSHGnTcdDgesVmtIYKE12VRKdjYvDox1u2kkFBRcgvfffzfEKEvZbgrwG2h9fb0QYOr5WFgs\n8esKiRVS4aHaDJuuXbvh+ef/FvZ1pHbnRjGasQCAm2+OTNcmDbQZLGORnEwZC6J5MZSxyMzMVL2C\nSEpKilnLY2vFbrejS5euOHNGzFiolUKMZCzEqw7twKKurhbBYDBm+gp+jfLx7lIizVjwr5ciZBH0\nMxbydLJRcyxAvKJ1u6PtCgmtTTOY8E0pJDWZTEhLS0d9vbwUIp7I9QML/jGJDSyAUKMslm2QZiwc\nDgd8Pq9wZa7nY2G1WuIyhCyWSDtztNqgjSBmLCLXWNhssR/RxLp1pAZZbCAeZSyI5sZQYPF//s//\nwbp164TJgABvMrNhwwbccsstcVtcayEvLw91dXU4fZr3s5CWKZRDufSuVoxkLJixT1PmYmjBUv3q\n4s3INBb864mbpt7JW2mQFUlJQ5r6jaYUwq7A1btCGjSDlfT09BCNhVZ7qpRx4yZg+PBLMWiQvuFR\nPMnKyoLFYhXcJxnqGQubzMdCLzBmpRA18y2jMKdIaXATS6QttlpTd42g5sESDqNdIU1BL2NBGgui\nuTE8hKykpASTJk2S9IJfgN1uR0VFBebOnRvfVbZw8vJ6YteunThwYD8ApcaCiTfr4fP5dK9WtGx5\npbDNIJqTohK2EcZCYwHIMw56GQvlyTkSoyu5j0U9zGZzk9rqRF2Luo+FVgCXlpaGU6dOyuacGMlY\n9OnTF6tWrYl4nbGEH3hnDxGsKttNAdGvwe3mp8jqdSiYzXxAEgwGdeda6KHXrhsLYpexiKYrJH6B\nhZrGgiy4ieaGhpDFACbg/OEHFliIZQqWhqytrQXHcYYyFnrum5WV/GCvaE6KSsxmM5KSksIYZDUt\nY6EfWMgNstj7GymFSNvrGhr4zIJRoyIpbLNUZiyYB4BWhword9XX1wmfUc/Ou6VhtztC9AHKIWTs\ncQDQ0FAX1q+BbbZ+vz/KwCJ+G2FqahqSkpLgdrtjlLGITGNhNpubfGz0YH+f0pIeCzIoY0E0NzSE\nLAbk5fEzQ1hKXpqxsFgsSEpKErwnou0KiUcpBOBLNnrizcgyFmL5QL8UIjfIiqSkYTKZYLfb4XZ7\nDHtfaL2OzWYL0bV4PB4Eg0HNUggLLOrqpIGF+gCtlohaxoIFFvJ2U/47amho0O0IAcSAJBr3Tbfb\nJTMSizXMy+LUqZNR/Q01tSskVi3iSsRSiBjotKZAl2hbxKeQ2c7o3j0PJpNJqC1LAwuA/8NmcyX0\nTiziVbj2VZCYsYhdKQTgswzl5WUht3s8bpjN5ohOiNLN2Ih4k52cWSnEaJDgdCZd1FjURWVb7HA4\nQzIW4To8WMupVGchOnU2LchpTux2R0iGSs0giwXCDQ0NYTNJTOTa1EFkHMfFvRQCADNm/BwnT56I\n6n2amrGIV2BhtfKOvurtpjTbg2heDAUWXq8Xzz33HD744AOcPXs2pKXsxx9/jMviWgsOhwM5OZ1x\n4cJ5oWNASkpKCioqygHoBxZGnDfZRM1YlkIAfo2nT58KmX3g8XjgdDojKjNIAwO9riGlQRbLWBjd\nmJOSnKirq4Pf74+qfdPhcKgEFvpCTBY8SltO4+3BEEvUBt4px6YDYvDHcVzYUgjLWDS15bSxsbFZ\nnCKvuupnUb9GUzUW8RBuAkw341CIN6krhEgMhrpCnnrqKWzZsgWLFi2C2WzG3Xffjeuuuw4dO3bE\n/fffH+81tgp69OgJgN9Ule2J0k1PX2MhzgrRorKyAhaLNSR4iZaUlFRBVyDF43FHLP5inzc1NVW3\n9KM8OYsaC+MZC2ar3dRSCMAHFspSiNjhoX5SZlfvzLsEEIMRpaFWS8Ru550dpR0cYleI3CBL/H/9\nTZF9n4FA04aEMfFra5ie2dSukHB23tHAZ/DEi5JIBwgSRKwwFFh89NFHeOCBBzBv3jyYzWZMnjwZ\n9913H2699VYUFxfHe42tgtxcXmchFW4ypFfgeicWtV50JVVVVcjM1LbJbipa7ptutyfiEz37vJ06\n6ZdrlOZUDQ2RlUKkV9DRlB+YV4MUMUhQz1iouW8y34DWUNNWC2LVnDelgbCehwUgdoU01X1TNMdq\n+cevqT4W8cpYAFDJWLSeDBrRtjAUWFRUVKBfv34A+BMtqyuPGzcO27dvj9/qWhGsM0TNuEp61at3\nYmHiOC0fC47jLs7fiG0ZBNB232xaxoLf5MOVa5Qn50hLIdJ1RZOxsNvtQhqeEU74JhWvsrf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OR0wpkzJ9HY6EKHDmno3FlfQ6NFIj53WloKzGZOeG+r1YTkZGfIWtLSkuHzeZCTk677erW1/HeZ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\n+OxWkgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f004fce6ba8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"(df.groupby('seconds_left')\n",
" .foul_called\n",
" .mean()\n",
" .plot(c='k', alpha=0.75, ax=ax));\n",
"\n",
"NBA_XLABEL = \"Seconds remaining in game\"\n",
"ax.invert_xaxis();\n",
"ax.set_xlabel(NBA_XLABEL);\n",
"\n",
"NBA_YLABEL = \"Probability a foul is called\"\n",
"ax.yaxis.set_major_formatter(pct_formatter);\n",
"ax.set_ylabel(NBA_YLABEL);"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Z8djcuXPxu9/9DoAgJBoaGtDc3Aye59HQ0IApU6agsbERL7zwAl599dV+e49D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OR0wpkzJ9HY6EKHDmno3FlfQ6NFIj53WloKzGZOeG+r1YTkZGfIWtLSkuHzeZCTk677erW1/HeZ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\n+OxWkgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f004fce6ba8>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Model\n",
"\n",
"The foul call probability varies over time."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"Throughout this case study, $y_i \\in \\{0, 1\\}$ denotes whether or not a foul was called on the $i$-th play, $t_i \\in \\{0, 1, \\ldots, 120\\}$ denotes the number of seconds remaining in the fourth quarter during the $i$-th play, and $p_i$ denotes the probability that a foul was called on the $i$-th play.\n",
"\n",
"Note that for simplicity, we have rounded the time remaining as reported by the NBA to tenths of a second to whole seconds. We can obviate the need for this simplification by using a Gaussian process instead of a discrete-time Gaussian random walk to model the time dependence in this data.\n",
"\n",
"We model the logodds that a probability is called by a gaussian random walk with 121 steps as follows.\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\beta_0\n",
" & \\sim N(0, 100) \\\\\n",
"\\beta_{t + 1}\\ |\\ \\beta_t\n",
" & \\sim N(\\beta_t, 0.01) \\textrm{ for } i \\in \\{1, \\ldots, 120\\} \\\\\n",
"\\\\\n",
"\\log \\left(\\frac{p_i}{1 - p_i}\\right)\n",
" & = \\beta_{t_i} \\\\\n",
"y_i\n",
" & \\sim \\textrm{Bernoulli}(p_i).\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"seconds_left = df.seconds_left.values.astype(np.int64)\n",
"foul_called = df.foul_called.values\n",
"\n",
"n_sec = np.unique(seconds_left).size"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"PRIOR_PREC = 100."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"seconds_left_ = theano.shared(seconds_left)\n",
"\n",
"with pm.Model() as nba_model:\n",
" β = pm.GaussianRandomWalk('β', tau=PRIOR_PREC, init=pm.Normal.dist(0., 10.),\n",
" shape=n_sec)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Transform logodds to probabilities, specify observation model."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with nba_model:\n",
" p = pm.math.sigmoid(β[seconds_left_])\n",
" fc = pm.Bernoulli('fc', p, observed=foul_called)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Inference"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"@contextmanager\n",
"def quiet_pymc3(quiet):\n",
" if quiet:\n",
" loglevel = pm._log.getEffectiveLevel()\n",
" pm._log.setLevel(logging.WARNING)\n",
" \n",
" yield\n",
" \n",
" if quiet:\n",
" pm._log.setLevel(loglevel)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"N_SAMPLES = 1000\n",
"N_TUNE = 1000\n",
"\n",
"def sample_from_model(model, n_samples=N_SAMPLES, n_tune=N_TUNE, seed=SEED, quiet=False):\n",
" with quiet_pymc3(quiet), model:\n",
" trace_ = pm.sample(N_TUNE + N_SAMPLES, tune=N_TUNE,\n",
" n_init=50000, random_seed=seed,\n",
" progressbar=not quiet)\n",
"\n",
" return trace_[N_TUNE:]"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using ADVI...\n",
"Average Loss = 2,955.1: 100%|██████████| 50000/50000 [00:53<00:00, 937.33it/s] \n",
"Finished [100%]: Average Loss = 2,955.1\n",
"100%|██████████| 2000/2000 [02:33<00:00, 13.07it/s]\n"
]
}
],
"source": [
"nba_trace = sample_from_model(nba_model)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"* Automatic sampler assignment (manually configurable)\n",
"* Automatic initialization of HMC/NUTS using ADVI"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Model diagnostics &mdash; posterior predictions\n",
"\n",
"To sample from the posterior predictive distribution, we change the value of the Theano shared variable `seconds_left_`."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"N_PP_SAMPLES = 1000\n",
"PP_OBS_ALPHA = 0.35"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1000/1000 [00:06<00:00, 147.16it/s]\n"
]
}
],
"source": [
"pp_sec = np.arange(n_sec)\n",
"seconds_left_.set_value(pp_sec)\n",
"\n",
"with nba_model:\n",
" pp_nba_trace = pm.sample_ppc(nba_trace, N_PP_SAMPLES)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
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nlVPbXX5jRMLC6XSFpJranR6e/zCbQ9Ui5ecDhWi1WkaMuACDwciePbubrClk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kAAAg\nAElEQVRKIu644w5cddVV2L17N+655x7s2rULzz33HHp6enD33Xcfz2s9pVDOG6CtiFhIkqRO1pU0\nFtpCW37H9/q7Mzg2EcP5G5rxyQ9sQFZk8PIQcYvsaPbA57Yb3q8vu+xq8WFrbyNGphOIpwV8/Mp1\n6GnTHB0FQcD6AjHpL3I3XIhnkRE59La7sLrNhz19YUwvlKbB6I5aT6biqTwGZskE/Oo70yVto6sj\nFlltF98TQmezC1mRQzSpRQ4GpwgZagnweN+5q8CxDJ7ZM14yUfeNRSGIMs5Z22gaJWoOGk2y6CJH\ny00BLSRdCceOHQUAiI4WhBMyDoU9iMa0hYtWmujhcDghSAwiGQ5r2/0GvQwAdHWtRkdHFwKBIBiG\nwXu3rUIqK+B3u2fw9GAD3pniwUDBxZvJLr6jyQOGASbnKUmyZpDFcSxmUza8dXQea1f5cd3ZChrc\nilpFoE8tLGUXX4xiYasIMq4CHgc6W7yw8yxm4xJ8Ph84jsP+Y/N4491ZvLBvEv3jUQQCASiKgrGp\nMAbGY2j2KWDSJDU2MKlF27J5EXMJUpINABNz5TQWxujSUroRy7KMTCEC01ggFi4Hj84GBsk8h/0D\n82U/m8mkYbc7wLIsRqYTePXAFDqaPfjQRaQp49wiIuyJcApelw08Q56vPmJh4zm0hxxQCr1DKkUs\n6mmQOhZDVcTiH//xH3H55ZfjG9/4BtatW4fHHnsMv/jFL/Cxj30MTqcTra2tuPvuuzE0NHS8r/eU\nQbkIQ8jvhI1jVGIBaKH8Sqr6xVon5wQJv3p+ADzH4OY/WYcrtrVja2sSOZGBIMrY2BUs+Yx+MmRZ\nFh+6pAcA2SFdvaMTgDF90RJ0we+x4+hY1LAg03Dx6hY3rr94NRQAT7xeGrUwswh/cd8EZIWBg1cw\nH8/hnYKAjmpKqpmc8/k85nTpge4WEmmYnNcW+KHJOBgoaAsSU58LN7dgaj6Nw8PG3hI0DbJVRyz0\n32Frkfum3hyJmlgtFrFIJOKYnp5CKNSImRhZtPISi+f3Tanno5UmejidDsxneChgStIgAGk4ddFF\nF6uL+J9ftR7f+V+X4boLV8HJyxBkFp3+HAIeEvmw2zi0hdyYmEtDUapPhai6D4bF4bAbDAPcdu0m\n2FjSOZUSiwEdsaBVIctRbqpVIRXGky5iwXEsVjW5kcixcHuI3uKRlwZBkwi/fWkQPh8J6z/27NtQ\nADQ502hwkjF5TBeNG5iMQwHQHRQBKJiOmi/MgpA3kHRNT2L9XmVZQkYgVxvyaxqGc7tZsIyCB3//\nrqrvKUYmk4Hb7SpELo9CAXDLVevhcTng4iXMJ8p/v7m8hHA0g85mj6FDqh69qzTfCjMPC4A2uasT\nizoqoypicezYMXz1q1/FSy+9hC996UtYt660LXhLSwsefvjhZb/AUxXlUiEswyDk45HKczrraTJh\n0WiEWRMyzT3PfKF94vVRRBI5fOCCbrQEXcjlcugO5HDVWQ4EPHZcsKml5DP6hYvjOKzrDOAf77gQ\n/+vGs9XFQ08GGIbB+s4Aosk85mPa4jkaJv/uafXgvA3NaA258erB6ZIJsDhiIUoynts7AZ5VcMV6\ncr6X9k+S52Rhh5vN5hBO29Dgc6C90Y2eVhLin4wUCJssYyycgs8hwe0i13D1ji4AwDNvjRmOdXBw\nHk47eRa0fb3+GvweOxw2TnXf1O+eqYnVYsTi2LF+AMD69RtwbCIGlgFsrIxXDi0gnRVLqgwoHA4n\nwinyN+riuhgafA5cd3E3ruyJ4r2rozi7JWUoBexq8SKbl6rySQCMHXkPjQtI5nlcvLkRXS1eiCLp\nzdLS4ILXZTMQi+WtCtHEmwCQK6QOPE5yjtYAIV95xoO3jsxiPJzExVvasLW3EUdGoyoJnYiRz111\n0Qb47BLsPGOIsvQXUojdjTz8DgXzSaVEg6EoCgRBMI1Y1KqxSOcZMAwM4siWgA2bm9JIZgT8eOeh\nEtKSz5Mmcy6XG/v653B0PIbt65twVk8IPM/Ba5eQysnI5My/48n5FBRowk0AJQ6em9c0AwAcvAKf\nyzzVsVjPoDrqAKokFl/4whdwzTXXGNz/ADLpvvnmmwDIJHDhhRcu/xWeoqjkDdDgYSEpDGAjO2s6\nUVaTCjGb/BfiWfxx9wgCHjuuv2Q1AK3U9JweDx6463Js7G4o+ZzZZNjR7AWv03gUu29SdbheZzE+\nnwMDBd2tXrAsgw9e1A1JVvDUm8bKgOJjvbp/ErFkHl3+LFa3ONDd6sW+/jlEkzk1f1/NQjQTy0OQ\nWGzpCYFhGPS0k93UdIScZyKcgiDKCDhElSitafejt8OP/QPz+O/n+iFKMmYW0piNZLClJ6Q+A57n\nDVEThmHQ0kBKTumion+WpNtmZfHm5OQknE4XmprbMDqTQGezG72hDLICeWbFvggUdrsdkbwLdp7B\n2lXmO0YzENID+B0SONY4vroLTaSSgr3K7qaEWCQzAl7rz4BnZbx/OxEXSpIEnufAMAzWdQQwH8+p\n5PJ4VIWo1S4iAwaKmrIIOgsmUxkOj748BJZh8JHLe/DR96wBADz99iy277gMCxkb1rT7sb6nAwwD\ntPgZTC+QxRsAjo6RaFZ3iwtNPhaizGB6PlV0LeSZ6ee+pTQhk2UZqRyDoNdh+B2yLIeeYBbbekM4\nMho1iDIBzRzL6XTiyTfI7+5jV/QCIHOH104rQ8zTORM64SYtNaVaDYoNXQ1gAAQdAkZHh2EGkgqp\n6yvqqIyqiMWtt95q6r+fSCRw6623LvtFrQSoYVqT3hgBF9md5xXyw6ULrSberJQKKZ2sfvXCAPKi\njI9dsRYuR2EXlyt1sywGDd/Svg9mKO4Xsr7TqLMQRAkzUQF+hwRPIRpwyZY2BL12vLB30lAhQo9F\nF86dr5AQdU8wC5fLhSvO7YCsKHjlwJQuDbH45Dy+QHZvND0Q9Lng4iXMxkkTOCq6CzpFQxTgM9dt\nRmvIjSffGMN3frEXrxwkqYhzerVKApblShbclqALOUFCPJVXn4veQ4L2PikHQcjD7XZjZCYJSVaw\nriOInmAWThvw1JtjiCZIxKNYY/HivknEMwq2rWs2LDqLobhsVV/OTAWcibzNQiqExWMvDyEnKNjQ\nmIHboUWX6PdGqwho1EJz3ly+qhD6fDJ5wM4pEAvjysOT5/fSO/OYXkjj8q3taGlwo6fNj/M3NGNg\nMo4/7pmHrADnb2yGx+MBwzBodMvqNYuSjMHJBHx2EUGfC20NZNwcHTVqHLRUmEYCa21CJkkSZAVI\n5zV9BQUhbMAtV65Go9+B3706hL5RLY1HyUA8Z8PR8Ri2rAmho8mjXhslFlPz5iWzE3NEuNnZXD5i\n0eBz4K9u2oJt7Rn09fWZksR6KqSOalDV7KUoimlTp2g0WjI4zxRUavzjc5AfZEYyll9qGovyzpvF\nk9WBgXm8fngGa9p9uOycdvXvNE9aHEUyHtNYHmeGYu+J7lYvHDZOjViMTCchK0CDS1Cv0cazuOmK\nXuQFCf/00z14cd9EQTOgCUEHJ+PoG4lgY5cXHrsMh8OJi89qhd3G4qX9k2CqNBmSZRkzCfLezYXy\nUJ7nEXSKyArE0npoipCboFM05MLbGz346m07sGNjM46Ox/D7QjXLOWs1YsHzfIlgVt+MrLgBFa0M\noRN9MahY12azYWCSPMMN3Q1wOWw4q01CNi/h+X3ThWevXevoTAK/ePYYvC4b/uxPSlONi0FPUvSL\noEYsquueqygKEjkWz++dQMjLoyeYVQmxJIkqaSkWcB6PXiE8z0NRFKTzCpy8rJJpRoiDZRTEUgJ4\njsENl/aon/3Ie9aAAfBWocz0/A3Nasmvz0Z+MwOTMYzNJpEXZTS4RDidLnQ1k03A4IRRuKwRS+13\nVqt4U5Ik5EQWCoDGQDGxKHS5tTH4yw+fDQYMfrTzMNJZ8iyoD8r+EXIPV5/fabgej0osjBGLXC6H\n5557GoPjhDCtatI0FsU9RwBg6/pWbF7fg0wmjZGRYcNr1fYMqqOOiiPkzjvvBEAmjS9+8YuGiVCW\nZfT392P79u3H9wpPUVSy4HbzZDKK5xh42NJUiJnGgk7Y+uNlciIefvIIOJbB7R/cDFZH7uiCp3fh\nK4ZWd794u3O1jIxlsXaVv9CkS1AXjgancady2Tnt8Hvs+NHvDuGhJ/owMBHHx9/XA4Dc77N7iLbh\ngnU+RCbIdbocPC7c3IpXDkyhfzxecr9mSKQyWMjwaPIy8Ltpd1MOAaeIqaQDQ9MJ0sGTY+BzSCW6\nBZeDx+c/ejaefnMM//P8AHrafWjw6R1A2RJDL337dK6oQoFGiHK5HLxeb8n16lMnVCi4riOAxKQb\nnXIKQ75m7Dq8gAtW8VqPj5yIHzx2CKIk4zPXn62WIVqB3a7Zqesn/oDHDp/bhmhGqWqHLYgK3hp3\nQlYUXL0tiHR4BpJEIkP6Pjc97X5wLKOLWCyfeFPvG5HNSxAlBQ6njGw2i1wuh1w2jUavG+GEgivO\n7TAs0p3NXlx0Vit2H55BZ7MHrQVfGbfbDU9iDoATx8Zj8BaibyGXAKfTiZ42G4AIxmaNO34abSwW\nQgPWSZS+IkQv3AQ0IWUikcC6zi7ccFkPHntlCL9+cQC3XrOR3LvI4J3RFFoaXIaomz5iMV1ELKLR\nKKLRKMbDLEI+J9xOHul0GhzHGZxw9diwYROGhgZx9GgfenrWqKSxWPtSRx3lUHGENDSQHaKiKPD7\n/YZFzGaz4fzzz8fNN998fK/wFEUlTYSTywPgsZCU0O7X3lOpKsQsYvGbFwewEM/hQ5f2qDtPCi1i\nYT45AKVOgebvKXXL3NAVxLsjERwbj6kLR4OrtMzsnLWN+NrtF+A/Hn0HrxycKqQaGoGjWQBZdLV6\nsSrIqMQCAK44dxVeOTCFlw9Mow2LT86Hh+aggMHqZo0wMAyDRo8CzAFHx6KYCKfQGiA+G2YRHIZh\n8IELu3HehmbYbcZnwbJcyc5TNcmKptEEMpnOJwQEveyiXhb6XgoDk3E0+BwI+Z1wudyIxWL4yGWr\n8Z9PHMWusQCS3AJua87hZ8/0Y3ohjQ9c0IVz1zVVfB7loNdr6L9vhmHQ1eLF4eFIWcMwPQ5Mcohk\nWFx2dhs2djqxN0zGZHFnU4eNQ1eLF8PTCQiiVNVie2wihh8+9g4u37oKH76spyQKGk/nkc9LhXA7\n0XLEUmRcOjgZ+Xwe0SiJKGzudEOeEFXNkR4fec8aHB6J4MrtHerfPB4PbFwYbSEnhqYSakqRtA53\nweVi4LVLmIrkICuKSuLNIha1aiwkSUJGMJaaUlCjr4WFeXR2duH6S1bjrb5ZvLB3AhdtbkEmk8Zo\nzAlRUnDV+Z2GTQbDMHDbWdg4BVNFGgtJEpGXGGQEBu0h8plMprT1uh4ulwurV/dgaGgQY2Oj6O5e\nbbjfuodFHYuhIrH41re+BQDo6OjAZz7zmRKxz5mMSuJNScjDY+cxF8sDfm3RrqyxoHlbMvn3j0fx\n/NsTaG90G0K9FGb9N4pB3RMrEwujLgLQdBZHx6M4NhGD2w64eNl0p9IUdOH/+eR5ePTlIQxMxjE/\nPweO4xBqaMAt12xGZKIPgEYs1rb70dnswd7+OVy7vlTfUIx3R8hCsrbNOBE2ehgACnYfmoYkK2gJ\nkHus1IG1KVg6mZJUiGRI9xn6cNgF7J324fEfv44ta0L4+KVE51HO1pvu6tIih3gqjx2Fah3629m2\nxotPXtGEnbuncWA4ib//wWsQJRk9bT786ft6Kz6LStD3sShesLtbfDg8HEEkzZRNawLA/mNz6J+z\nwedQ8IkPbMDs9AQAI7HQR796OwIYnk5gZDqJ9gYyNsoRi9loBv/26wNIZgQ89soQcnkJN1/Zq17L\ngYE5/HjnYbAsg+s2alUYsYJXiYOXkctlEYkQ3cHV56/CbR/uNL2X1gY3vnvX5Ya/ud1Ej9DV5MT0\nQhb7j83D42Dg4mU4nU4SBXNImEjwmFlIo73RKLw2aixq624qy5IuYmEkFg0NDWAYBgsLhXJsjsXt\nH9yEf3p4D/7zj0fwgU0CRmIOOGwcLtelRPXX5HcqhX4g2nUJgqCWvnNSnER8cln4/aVVZHps2LAJ\nw8ND6Ot7F11d3WAYxmC1XkcdlVB1VUidVBhBf1xm4s18Poegm0EiI0KQGHXRLjaHMjueJEkQRAn/\n+UfiIvjpD2429CKhoPnmSqkQAAgGG9TGTGbQ6yIo1q7yg2UYvPnuDGKpPJo8CjiOLS8A5TncfOU6\n/MMnzsNVG0RcsTaL//0X5+G8TS0lLdMZhsHm1SFIsoJE3raoxmJkNgUGCnraPIa/uxw8fA4FqUIO\nuqkQ0NFrLKpBcT8MAGjwE8X+oaEF/O4Ai4m4HTae/P/4AjlfeWJBXp+Nke+aahHowpZOp9HqZ3F5\ndwx/+p4OuB0cPC4b7vzIFkuCzWJo0anSSZ9Gu+I5vmx78Egih5/8/l2wjIL3rJPgtPMGLYGZPkiv\ns6jk7ZDMCPju/+xHMiPgxveuRXujG0+8MYqfP90PSZbx25cG8d1fHUAqKyKRFhBNyyrh1SIWCnK5\nnEosgsFgWYJkBo+HPP9Wf+GeFAWtflL26XS64HZ7EHCS725E12hPq+BZukGWLMvICNTO2/i75TgO\ngUAA0WhEHYu9qwK4ekcXZiIZ/H6/gKzI4fKt7Wq0RQ+e5+GzK5BkBXM6a29JEhHPFcp1+RwOHtwP\nYPF5w+PxoLt7NRKJBCYnNYJJz1VHHZVQdoTccMMN+NnPfoZAIIAbbrih4kF27ty57Bd2qoNYHpd6\nA+TzeSiKggYPh4mohGSeUxftSqFETWMh4YW9k5iaT+Oq8zqxrtOcFORyOXAct+iP/L3vfV/F14s1\nFgDgtPPobvWq1RaNHrliJEAPu91mWLzMWqZ3t9KFzlYxnCxKMqYWcvA5JHjdxmgDz3MIOkUkcoVc\nuZuo7Ys1FotBn9Ki3wtbKDmdnEvBwSu4oFPC+6+4GP/40Ft4Zm8YZ/kWT4VMxch90eoJSszT6RRE\nUQDDAJed3YqrLlyHQNCNbKq6/iPlUCntpRELDpHIQok2RJYV/Oh3h5DMCNjalkXIY+ziKUmyGknT\njzd9Zcj7trUUjmUkiqIk4z8eOYjphTSuvbAbN1zagyu2rcJ3frkXz749jn3HwpiP59AUcGJTdwNe\nOTiF+aSC5kARsSiINyORHHieh8dTqm+pBErsmrza9TW6SQqHRv2afRwQBkamE7i4YG9PNRb6cVWr\nj4UkSTrXzdJIY0NDCNFoFLFYFA0NJDL2sfeuxd7+MOYKvjJX6USbevA8B49dBMBhaj6Nswt/FwQR\niVwh7ePlMTo6YngelbBhw0aMjAxjcHAAHR2dKmmuV4XUsRjKjhC9b8U111xzwi5oJYHnS0v4qL9E\nS9AGTEiYSdlKNBbm3U1pKFnCkQmyK/vgxd1lz53L5SqWmlIstqvjeR4Mw5QIGNd3BlViYaavKAeb\nzQ5B0Jw7s9mMakNMsbrgrRDLcZAk43klScK77x6GIOQxGyPCvaBXLLlXjuMRcKQwBjucdg4em4A0\nKlfJmKFc6eCfX7UOY7NJJMffRHNjCGva/di+vgl7++fQzNnQUcbLgj7HyYU8eI5V75WK89LptNHN\n08bB57YvG7Ew8xhoa3SDYxnEczwWFubR1WUcV4eGF9A3FsX29U3oZPvBMORZ6/u5mJHiRr8TQa8d\nxyZiunGmRSxSWQEPPdGHvrEozt/YjD+9kqR6/B47/vdfnIf7frkPIzMJbO1txGdvOAuj0wm8cnAK\nkTSjEtl4gVi47cTSOpsV4fcHLEUrAI3Y2ZGFx8kjlRURdBj7ZaxqdAKDiqFnSLGnBlC7eFOSZGQE\nFnaeMY06hEKNGBoaxMLCvEosHHYOn/rABjzwqwPoamDQFjKPHHMcD48tA8CBqQWN2AuCgESeAwNg\nx9Z1OPzOAQCAy7X43OHz+dHc3IJweBaJRLzegKyOqlF2tfjCF75g+u86NPA8X1LCl8uRifCsLi/2\njMgYjCjYVjAR0jd4MjsWQHbOw9MJBLz2itUB+XxOtS5eChiGTOLFHUnXdwbw9FtjpNrCJoDny2s5\n9KCTDl08s9lcySTW1ugGz7GmlQpzc2EcPUrSQMNRBwAvGlxiyS6b53kEHGSi62nzQRAWwHFcxdJa\nM5SzUj97TSM2dQXwu4k31Hu68T1rsa9/Dn1zbmzsJDvIvCDhl8/2o388hjs/sgWSJEKUgZloHr0d\nATW9oUUsMmoIfTknaLqjNhUGcyxWNXkwEU4gPFfai2K4UK77nq2rMHiwT32G+gWUjnM9KaZGWW/1\nhTEb1ca4LCt4cd8EfvvyEJIZAb2r/Pi/PnSWQXDoddnw95/YjqHJODaubgDLMOgqkLB4jlOfTSxJ\nxpHPZUM8Hoff70IwWGpfvxhcLhdYlkUmk8b5Gzvw/7d33vFRVen//8zcKcmkkkpCaAkkUhISECGE\nIqDCwrILrrj0FVbaT1ABEf0CUqQJK4KxgCAufkUsrICiLuqiX1dRIQqCNCGUJLT0NpNk2v39cbl3\n7p2ezEySSZ736+VLcueWc8+cOec5T71YUA41ShEQYMlwGhYShCBlJa7dqhIcOPn8PdahmQzD1Ftj\nYTabUWuUIyyIsSsY8SXgS0tLkSRyt4kL44q/detiX1sBcL8HjUIPIEgScmo0GlBVxyAqTI3kLl1x\n9XIudDqtTTpvR3TunIiiokJcuXJZEHbshcsThBgaIR6gVCoEDQUPryIPCQrAQ0OSYGZlOH6FL0Lm\nOI8F73RXVWNEWVUdOjvI1Q9ASNDkyk7qLlyoonRh7ZoQxiW3igsFaza4rf60pAjnUhAbDHobbYOC\nkSMhOggVNYDRZC2Ycf3ZrVsPBLbhvNH//MAgGx8fhUKBsAAjBvSIwQP3dLhTLbR+2gr+PoB9tbZ1\n6u2EmGD07RaDijoFLhcaUFheg3X/+zO+OXkD14u1eOHdE8gv0qG8VgGWtfggAJwpSC6XQ6fT2pTh\n9ga8b4mj76lj2xCYWRmuF1bZvGvebS55Uvs7NVh4gULsUOzIvs6/44q3cnDkSji+OmPAyreO43+/\n+B1Gkxnjhybh6Um9oVbaCjwBKgW6dYoQBI7gQCUiQlSoqFMIAgxvCgkNsny3YWH1FyxkMhk0Gg10\nOh0e+cNdWD41HQArERiCgjg/i1q9CUVlNairq0NRUSHCw9tAxqhwIa8MXx7Px6ncYrvRRK7Q1eph\nMMsRFmT/OwoODoFSqUJZWankeEFBHtoEGpHUybEGk2EYaJRmyOUySZKsCi33zLhIDeRyOdLTM9Cm\nTYRNuXlHxMe3g1odgGvXrglznbtmUaL14tTHwl1ao48FAAQFhaCiokISvsUvjCqVCpld2mL/12eQ\nVybH7/nlNupkaw99hmFQWGkCwKBznP3qguJnOIsIqQ9Kpa1TX1iwGvP+koqoUDWOf3/ZbVOIpV6I\nQZSIx1YA6hAbgqu3qlBulYGY15yEhIQgv+g6AtUMOsTZLiQMw0AuAyYNT4RGo8En5/RuqXetsYQO\n2qq17aXe/vPAzjh+7jZ+KWBw4q3j0NUZMSQ9Hu1jgrHni9/x/neliLjzvknxFsGCT9Kk0+kQGBgg\nmKC8BT/ZO4oA6hwXiu9O3URZLYOysjJERVnCWq/drkJwoBJhQdKEamLHVkcRTQPT4lFVY8DVm5X4\nPa8EV0tYANUYmBqHvwxJRFhw/cZouygNTl/RC6XSK7R1UCsZBGuU0N6xUDREYwFwfgWFhbdhNBqF\nFNniMaPRaBAeYMSNKjW27DsFOWuEThcKmUKJd459K7lX54gA3N2hfoJF6R3NZZjG/m9JJpMhIiIC\nt2/fumPqVINlWRQUFEClUiMmxnEkB8Nw4dbRYQG4VaITTJG/5XNjmC+D3rZtHNq2tY0qcYRcLken\nTp1x4cI5IWEWOW8SrnDqY0E4JzQ0FDduAJWVlYJgwZsA1Go15DIZ+nZkcfgcsPc/FzGqhxksC/xw\nthifHzuFlA7hmPPnnsL9GEaB4jublc5xjjUWFuHFO4IFZwox2Ag6GV2jhfdxd3ctrhfCZ6e0J1h0\nvOPAWVHLSApf8c5yRjODW6U6dLujJrdtsyUVOcuyMBoNUCrrbxpyluiM1+KId2hxkUHoGsvg99tm\nKBVmzBjVDQPTuIk6QMXgzUPncLOa+166tJO2R6PRoKioUDA/eRNeoHM06fOCakUt52fBCxa6WgOK\nK2rRo1MbScl07v8WJ0VHWWM1AQr85U7Nio8+2gd1UAT69cu0G9rrDnERapy+AvBuAhVaPcKCVFCr\nubbIZDKEhjqOcnKG2IHWXvZJjSYIMUF6XKsMQVlVLcwmM1iWQaBMhm4d26Bj2xC0iwrC4WP5uFJU\njfIaM/pm1iAqzL13Lavifku8AGePNm04waKsrBRt28ahsLAQen0dEhOTnAqivG9NTLgat8tqUFGt\nx/ViLU5cM0LNmHFfX8faDld07pyI338/L+QQIedNwhVu+VgQ9gkN5RaOqqpKxMZyhZp4dSGvTYhr\no0R8SA2u3QKOqpS4ejsMFRevAgB+vlCEmjqj4MjFMAyK70yonZwKFo41AQ1BrGWwV2iOb5t797KY\nQpylDu4gceC0JFjitQS3yrn/OyrGJTZh8GXI6+u4CTgPHbQ47kkXgqyUQBjqijF+xN24q3OscHxA\nzzhcvZKL/5ypQ3R4oM1unV/YamtrhLHjLSzp2+1/TwnRwVDIZSi/I1jw8GaQDrEhosyw3AImztfA\njwNnWVwZRo5ApbnBQgUAtA3n+qy4moXZzKJKa0B0u0Co7/xGQkNDG5ygiY8k0el0doXeoCANglVm\nPDI4CN2798Tnnx9CZGQUhgwZLLnP3XfF4IW3juBqKYNVbx3HEw/1chi9JYYXLNqEOB6nkZF8oixO\nsCgo4AqOJSQ4Fwz430PMnf7Lu12Jf35+DmYW6NVWJ2QabQgajQZt28bh5s0bkuqSxS4AACAASURB\nVGcRhCPIx8IDQkK4xbGqylKIy1qboFKp0C1KB6VCjl/zDKioU+Ceu6Jxb0Y7mMwszl612FMZhkGZ\nTo7o8AAEBzre1XjfFCJ1uBRjL8zQGfwCp9dbBAt77UyICYYMXG4Fsc2fb0NBCfeOjgQLftdkMBjt\nFopyF2cFpXhfCOvcGG1CNegRo0NUiO0C1zGCRVaHCjw2rqfNZ2KHOe9rLBxHhQCcX0v72BBU6hkU\nFokFC86+0CE2RNBY8CnnxUIXL3g562O5XO5xEbLYcO7+RZUmVNcYYGbZOxoLTgBoqBkEsAh2Wm21\nQ40F97kW168XAADat29vcx+1kkFWEpAeVwNdnRH/+8UFt1KZV+i48dQm2PF3Hx7OZTsuLS2B2WwW\nKuXyAocj+N9DVCgnQLz1yRnkXq9EhzZmtAv3PM16586Jwr+puinhCspj4QEhIaGQyWSorLQVLPjF\nVKFQIFBpxkODO+K/J66iQ3A5po8Zgmu3tfjmxHWcyi1BnxTOdqozMNCbZE7NIPae4SmWXBa2yb7E\nBaHcQaz9sOwKbXewaiWDcI0MlbWMxIGTX8zzCjnni8R4+ztBi8bCKGg5GqaxcGwKsS5AxsPb5Xk7\nvRiDwYA2gWa0j7X9DsUOqN4O2QsJCUXbtnGIj2/n8JzOcSG4crMSRZVGaLVaBAUF4ZqgsQgWRS1Z\nayxMgg+KM22BTCb3uFZIoJKFijGjsMIgOG5yggU31vkyAw1BnKSM/77FPhZyuRwBAYHQ6XTIz8+D\nTCZDfLz9SAyGYdAhrBaq8I44dq4Qv10plRS3s0eFlntmRIjj361arUZwcDDKyspw69ZNGAx6dOqU\n7FbYOABEhnDj6lJBBYICFOgVV+WVsRYb2xYaTRB0Oi2l9CZcQnksPEAulyM4ONhGsBAnruL7sG9y\nONS1MhQXGzmHqLgQBAcqcfpyieDbUF7LAGAFRytHWJtbPEXsF2ENH2boflSI2HmTOxYQYL+d0aEM\nynQsisp0CL6TGZFLMAZcvVWNyNAAhAXZFxb4XZPRaBR8IRoSFeLcFGI/bp/fPVtHBHHXGBxqI8RJ\nibytsZDL5RgwYKDTczq1DQVwHRV1DEpLSxAUFIS8wiqolQxiIzTQ3XHgtQ435c1NgPNxIJPJPK5u\najabEKo2olgrF6IbwoJUSEhoD51Ohy5duqC83H5yMlfw2Te1Wp2gWbEWejUaDUpLS6DTaRETE+vQ\n3CiXy2E2m/GHAR1w7FwhPvvhml3BQuy3VKEzAmARHuLchNmmTQTy8/Nw/vw5AEBCgq3WxBp+vokI\ntiz6E4Z3RenVY1AqPa9ALZPJkJbWC9evF9Q7ORnR+qA8Fh4SEhKKqqrrqK2tRUBAAPR6vcSp0mIa\nMAhOijKZDDIAPRMj8OOZ28gvrEaH2BCUarn6F7xjoyP4NNnect50rrGoX2ik2MeipoZbjOxpLAAg\nJkyJ328ZkVdYjc4J0cLz9FChusaAbh0d7075fuUEC080Fs6iQmwrWwIWAYbPWSK9xuiwr8Qai/qm\nHvcGvAMn72cR27YdbhbrhBTu/GLLL4QymQxyudxhgixruMXWM42FwWBEmNqEYh3w22XOTBgWrAbD\nMOjWrfudvm2YYMHXBNHpqgHIwDCMzZjRaIIEHxRnCzrfDwnRQeiZGIHfLpfi0vUKIfzWbGax7eBv\nOHmpBAnRQegQG4LiSiMCFGYoXZgSIiMjkZ+fh/LyMgQFBQv5I5zBm/SUDIsenSMQGRaIAT3b4sAl\nAxjG+UbFXeLj2znViBEET718LPLy8vD111/j66+/Rl5enq/a5FfwSap4rYVeXwe12jJZ8ROX0WiA\n2WySTMxpd3Y4py9zE1lxNQCwXAZAJ3jbeZPf7djzsaiv86ZY+1FbWwu5XO5wwY8N5xZXcalqvd6A\nSj0nMDnyrxC3x2Qyeehj4dgUYqlsaa2x4N/RvsZCHJ4qRixYNIUDXFxkENRKOSpqlSgpKcH1Yi3M\nLCukWLeXwI1hGImPhbPkSPwu3hMMBgNC7yQ+O32F+12EOtBaNQSNRgOtVndnI2Ar8PJaDblc7nQR\nFY+/0f25fCuf/XBN+Py9IxeRc6EImgAFCoqq8e2vN1BrYBGkNLtMMCUWJNzRVnDtsYzjRX9Nx+Kp\nd8NsNoNlWcqUSTQ6bs1uZWVlWLp0KY4cOSJMOizL4t5778W6des8snv6O5bIkApERkbCaDRaaSws\ni7bJZBIc4wCgR+cIyACczi3BH/p1RHG1GcEqE5SMc3uqXl8HpVJZ7yyTjrAIP/YW1/r5WEgTZNmm\n4hbTtg3XTwXFlmQWBoMe5bXcDivJgX8F1x6LxoK363umsbA1hTjyseC/X2uNBcuyMBgcm0J4G35t\nbU2DzDaeIpfL0LFtKH7PL0NJWRlkN7msknyEjnW4Kfdv5k7mTdcCplwug8HgmWBhMhmFYmB81k1H\n5rCGoNEEoaqqCgYDEBlpW6KeF/5iY9s6HU/iUNzk9uFIaheKk5eKcb2oGueuleGrnALERwXhf6b0\nhkrJ4EaxFt/nnIGh6rpLIT0sLFzI7JmQ4DjbphhxSQAeXuNG4aFEY+PWyrRs2TLk5eVhz549OHXq\nFE6dOoV33nkHBQUFWL58ua/b2KzhBYvKykq7+SXEi7bZzEomlRCNConxobh0vRKXb1TCYALCA4w2\n6aWtqa2t85p/BSDWMtiLCqlfRUO+TDsfFeJMqxIcqESgwoQbJZwTJL+AlWrlYOQyYSft6DkA16+W\nXBsNybxpP6U3f2/uvtaCBe9HonfrfDH8wuVIq+FrOHOIDOU1DC7mcRoBvp6JJdxUqrEwGsWmEFdR\nIZ6aQgwIUpqhUlra4E3BgtdIAPZNdNHR0dBogpCU1NXpfcTRRDKZDKPuaC12HjqHvf+5iNAgFZ58\nKA2aACUUjBwdYkOQEqdAsMrsNGQX4PqxQ4eOiI9v53aWUUs+FotgYa/OCUE0Bm6NuO+++w7//Oc/\nkZGRIRzr06cPVq9ejenTp/uscf5AcHAIl4q7qkpQjYudFcXhlyaTySZUKzUxErk3KvHpD1cB8IKF\n44x+LMtCr6+zqZ3hCfzEY71QAnDLac/2fipotVoEBjIICnIsWDAMg1C1Cbe1JpRX1yFAwcJkBkq0\nQPvYYKjspIG2brPJJNZY1F/l60xj4Sj1tkKhgFwuFwRJ6/OdOWZyIaclTZYWmY84Kq9VoEJbBUYu\nQ3wUt9jy/hFSU4gcer2hHlEhnmksjEYjZDIgISoIl29yobDeNIWIHQ/tZWoNDg7ByJGjXN7Hornl\n3rdXlyjERwXh2u0qqBRyPP6XNJt8Hu74qfBkZPRxeY4YeyY9dwRdgvAFbmksIiIihMySYgIDG1YQ\nqCXBMAyCgoLuaCx4J0KxxsLiGClOBMWTmsT5Wfyay+0ew9Qmm8JmYviy7L7QWPALo5j6mkK4+ykE\nIcWZxkIulwtq77zbVdDW1OJiaSDMrHP/CkA6kVrX9KgPlvvYT5DlKPW2SqW26S93dogWjUXTTPad\nRILF7QoD4qOCoFRIq3Vap5k3m01u5TPxho8FP9463omMCg5UCoXcvIHYz8WRU7E7WAukcpkMDw1J\nQliQCrP+1MPu+OWFM2+ZMKXtsdR14aEy50RT4daI+3//7/9h3bp12LRpk5Bh8vbt29iwYQMee+wx\nnzbQHwgNDcONG9eFRFli2yy/MzUYOOdNazVox7YhCNUoUakzQC4DQtXONRZ87gRvOW4C4qgQxw6M\n9VGnihd4Zz4WnMaCe+aRX64j73Ylyqs10KhlGJru3PtcrPrlJ1NvZ97kIjzs31OtVkGn09mcDzgX\ncNq3b4/KygpERUXXu63eIDqMS752W8vCzEJibuJ339Y+FuKoEGeLojfCTQ0GA+RyOTq2DQVww6tm\nEMBasGj4b8hejZn0rlHo1SXLYc4JR/VWvIG91PT1jegiCG/hdhGygoICDBs2TCJYqFQqlJSUYPz4\n8b5tZTMnOJjbXRUXFwGQ5pcQJ4wym802k4pcJkPPxEgc/e0WYsKVYOT27f08ztJkNxRnmTcbYgoR\nL/DOJm+GYRCm5ibbU7klYOQyJLWpwZiszkiIcW7qESfI0uv1d+pvNCQqxLnzpqPCZkqlCgZDhaTO\nCT+RO2tHeHgbZGUNqnc7vYVMJkOntiH47QoXysk7bgL2o0J4LYTRaATD2C/3LT4XsC2uVx/4PCC8\n34c3zSCANJeINzUWPM7euz6mkPq3x56PBa9looRWRONCRci8AO/AWVTECRZiUwi/aNfV1YFlWbs7\nvtQ7gkV8BHedPc0Bj7PCXg1FJpNBqVQ68LGon/MmIN0huRIsAhRmdEsIRFBQMAakBOLy+RMI1rg2\n84idNw0GfYOjLMT3sYZb5OznAOC/Y71eL7yjoxTgzY1OcaEWwSJGrLGw52PB9Q+nSXDtdAjArgDt\nLkajCUqlEu2ig5CWFIn0rraRG56gVqvvjHVDg6rh8lj7WLiD2Wzmcth4saotj7OoECpzTjQ2VITM\nC/CChcWvwLIw8os2n3vC3oTbJyUaYwZ0QudIMy5fuObCFMLdx57PiydwFU4dm0LqI1i4q7GQyxnI\nZMCYu8Nx113dcPnyJZvrHSGTye5ELBih1xs8Wsz50D4xfBirIzWyOJeFtWDR3CdyPlEW4EhjIfWx\nADgBypWw4B3BwgCNRgMFI8eT43s16B6u0Gg0qKio8InGwhkmk8kn2grAvimEbxuZQojGhoqQeQE+\nSRaPdUZMhUIpRBDY2/UpGDnGDU5EdDi3QDW2jwXA7bIdOW/yi7i7iBdWZz4W4pTRgCWluLvaB4VC\nKdQK8WQxZxiFjY+FK4dQi8bC0mf+4oXPpfYGglRmobIuAJF/hEWw4Mcr18fOxwAfpuqJn4XRaPS5\nYJaY2AWJiUkefU/WY9cdzGZpHhtvwmf0FQsWlMeCaCrcGnF6vR7btm3Dp59+ihs3btiojc+dO+eT\nxvkLXGRIMLRarqCT9Y5bqVSgpoZz9HPm/CYuBe4IX/hYcM9WwmCosLGPm0zGevsuuKux4BcqflG3\npOZ2b8JXKBSoq9PDbDY3yHGTh8/VIIZviyOnVf554uyb/qKxaBOiRre2LNQyaWps+5k3bc0ijuDH\nTUMFC15L5OuspOJKnQ2lIRoLTzQ57qBQKCT+WZTHgmgq3BKft27digMHDmD69OmQy+V4+umnMXny\nZISHh2PFihW+bqNfwJtDVCq1jQ1VvOt1ls7XWXppnpqaGsjlcq+GmwKOs28ajaZ673j4naBKpXJZ\nWwIQayz4xdxdwYIRFnZPMlkqFLamEN4s5EhI4PtLnMvCnybyfokMEkJqJAmtnPlYcMddmUJkkvvU\nF4uzYfMWzADn0USOMJl8K1gwjEIyjhsSKk4Q3sAtweLzzz/HypUrMWHCBMjlcgwfPhzLli3D/Pnz\ncfToUV+30S/gzSHiOiE84t20s4mFFzqcTVaOahx4iqN6IUajsd4LJf++rsw11ru++uajEAs8nvpY\nWPe5q1A9i8bC0l/+orEAxAujRbtgL9xUPF5dLVBiH4uG4E+CmeVd3ReiOB8L31mfFQqp5s2VcEwQ\nvsKtUV5SUoIuXboAgJAMCgAGDRqE7777znet8yNCQjgnOHsVR8UTsjPBwp4DlhiWZVFbW+N1/wpA\nWixNjNFoaIDGgruXKwdT61wA/CLtrllD3K+eaCwYRmHT564iPMRRIZZr/MPHArCvHeMXSbHGTayl\ncNd5s6HZNy2CWfMXLBpiCmFZs1NTqKdwTsiUx4Joetwa5XFxcSgsLAQAdOjQQRAmTp486ZNFzh/h\nTSH2TBTiH7Yz5y1xYSN78CGrvtBYiKuS8rAseycNeX01Ftz7uqux4He4XNio0u1wPHG7PPWxYFlW\nstN2VICMx16FU3+ayMW1LngcVTflqU+4qT3q6upw5MiXKCjIt/u5JbS5+fefq9+qNSzLwmg0uuxD\nT7AWkMkUQjQVbgkW999/P3744QcAwLRp05CdnY1hw4bh2WefbfXJsXjCwsKRkNABHTp0tPlM6mPh\njsbCkWDBh5p6X5izZN/0PMohJCQU7dq1R+fOnZ2eZ9n1cc/R6w310jzUR03vzn3qU2fBXhp0PiTT\nl7tSb2HPR8CVYOFKje9KsCgrK0V5eTl++SUH1dVVNp/7u2DmjOLiYrAsK2g2fYFCoZAIyEajwS/6\nkmh5uDUbL1q0SPj3yJEj0bZtW5w4cQKdOnXC0KFDfdY4f0Iul+Oee/rZ/cx9HwvnDmG+iggB7PtY\nNCTrJsD1Rb9+/REdHYKiItsFhMeexqI+xdW8p7GwjcZx5S+hUqkgk8kkzptcBI1/TOT2hCne6VKs\nVRPntHAlvFnCTe37HfDJ3YxGI3JyjmPIkKES7ZQlPLL5Z4qsr/NmXt5VAECHDp181CJbU2pDHK8J\nwhs0aNSlp6cjPT3d221psUh9LJxFhTjOAglAqE3h7YgQwL6PhaXwlG8meplMBrlcDpPJJKSNro/G\nwns+Fra7T74fHPlYcInPVBJTCKdx8Y+J3CJMWbQL9lN6u+9j4SrclBfCgoKCUVpagvPnz6Fbt+7C\n5/6SBwSon6Oq0WjE9esF0GiCEBXl3UyiYqznD4PBYNeZnCB8jduz4JkzZ7B7925cusRlR0xKSsIj\njzyCHj16+KxxLQV3fSzE2STtYcm6qbH7uSfY87FoDBstH5HRkAql3owKAaQ1Wlz5WPDPlPaXwesZ\nUX2FPedDR9VNLf92LyrEUbgpn9ytd++7kZNzDOfPn0VsbCwiIrgKv/7kE1AfH4vr1wtgNBrRpUuy\nT9J584jr5wCWLKYE0di4ZQz++OOP8dBDD6GoqAhDhgzBkCFDhOJjBw8e9HUb/R53fSwAbsJypF71\nrY8FNymJ64Xwvh6+VKfy1TPrmxwL8G5UCGCtsXC9e1ap1ILGwmw2w2Qy+cVuG7BdhABxuKkjwcKz\nqJDaWq6vQkJCcPfd94BlWRw/fkwQKv0xXFes8XFEXt41ALDrf+WLNhmNRpjNZpjNZr8Zj0TLwq0V\nY8uWLXjiiScwZ84cyfHt27dj69at+POf/+yTxrUUxIulq8mZy57naGL2nY8FPwGJnREtphBfChZy\nmEzmeifHAqQmGk+jQgDpImHRoDhuj1qtBsuyEr8Uf5nIGxIVUp9aIfaora2BTCaDWq1GQEAAunZN\nwcWLF/Dzzzno3z9TGG/+YE5y18dCq9WiqKgQkZFR9fIfalibLM7f/mRWIloebmksSktL8Yc//MHm\n+MiRI1FSUuL1RrU0xD9uVxEDXJIbxz4Wcrnco0XUEZYoB9taA76c6Pmsl56aQjyZQO3t3uvqaqFU\nqpyqrsXl5i2mk+a/KAIWVb49503HPhauokJc+1io1QFCn/bo0RNRUdG4caMAv/9+oUXmscjPzwPg\ne20FIK1w6k+OsETLwy3Bol+/fjh27JjN8WPHjqFv375eb1RLQ6zadfVDt5cFksdXWTcBscbC86iQ\n+iCXy2E2m0TJsepvCqlP7gt7WO/eWZaFVqt1ucPknWj1+jrRbts/dojOwk3FfkD18bFw5bxpndyN\ni6Tqj4CAQJw5cxrFxcUA/MMU4q7zZl7eVTAMg4SE9j5vE6/BMxqNbmncCMJXOJwpvvjiC+HfgwcP\nxosvvojTp08L0SAnT57El19+SeXV3UCsYXCVIMdeFkiAW+zq6mrRpk2E19vHtUsOhUIhESwawxTC\n1zewFP2qf1SIJ/4VgK0jnlarhdlsdilYiHNZ8GYUf1gUAbGWxnlUSP2KkDl23tTr9TCZTDbOrQEB\nAejXLxP//e83QhE/f1kMuUyXjjUWJSUlqK6uRvv2HRrlncRaKH+qu0K0PByuGI8//rjNsQ8++AAf\nfPCB5NiaNWswefJk77esBSGXy4VJyJUpRJwFUnyuL7Nu8nAVTsVJovhMiL7WWJhRV1e/dN6AZQft\nqanGOv6fX+CCg50nMxIXIuMXDn9ZFO1FNdhP6e2+YOFsF887HtsLlY6MjERaWjpOnvxFiIzyB5w5\nWgPApUsXAfg2d4UYsUnPn8xKRMvD4ag7f/58Y7ajxaNUqmAy1bi0U4sXOfEiy4fq+SIihEelUqKm\nxlJKuzFMIfwiwi88DXHe9FRjYZ2oi88K6b4pxKLl8ZeJ3FmCLMc+Fg0vQsaPK0eCcWJiEmprayV5\nQZo7fA4We5w/fw7Xr+cjPDwcMTExjdIeceZei/Omf4xHomVBo66RUCoVqK11L9wUsHUK82VECI9S\nqUJVVRWMRiMUCkWjVJvk+4N/v/poLPiJ1FNnVuuCXNXVnMbCVfplcSEy3nHRXzQWvFAm3nG7qm7q\nSbgpLzgGBDhO7ta9u3/lxOG0kLbveu3aVZw9+xsCAzXIzBzo09wV0vZYxrHFeZOmeKLxcbuowTff\nfIPJkyejX79+6N+/P6ZMmYL/+7//82XbWhT8rtpZgizAMuGLIxQASzpkXxZ9i46OAcuyuH69AEBj\nOW9y78u/X320D4GBGq/sCK09/HnBIijIucaCdzTV6+sEE5IvInZ8gbMEWQ2tFWJx3rT1sWgMwbix\nYRi5jXbm9u3b+OWXHCiVKgwcOKhRE6aJ5w5y3iSaErcEiw8//BDz5s1Dhw4d8NRTT2HRokVISEjA\nY489hn379vm6jS0C/gfuTlQI0DQaCz4k7tq1qwAax8eCX6z496vPRMgwDIYNux+JiV08aoO1MFdd\nXQ21OsBlW3iNRV2d3u92iPbCTV0JFq7GgbVJSQxvylOrW041ZOsIrqqqShw79gNkMhkyM7MQEhLa\nqO2x+FiYyHmTaFLcEix27NiBZ555BuvXr8f48eMxfvx4bNiwAUuWLMGOHTvcftjx48cxZ84cDBo0\nCCkpKfjoo48kn7Msi+zsbAwcOBBpaWmYOnUqLl686PK+hw8fxqhRo9CzZ0+MGjUKX375peTzN998\nEwMGDEBmZiZ27dol+ezs2bMYMWKEsLD5ioiISAQGalzW+RAnuRHTGD4WwcHBiI6OQXFxEaqrqxop\nKsTiY6FQKJqkMqhYmDObzdDpXIeaAhYfC4NB77K2SHPDWVSIo5Terkt+c9fZiwqxCMYtR7Dgs8by\n5Ofnw2AwoFevDJ/WBHHWHkBqCvEXnx+iZeHWLH7jxg0MGjTI5vjgwYNx/fp1tx+m0+mQnJyMpUuX\n2p1gduzYgV27dmH58uXYt28fIiIiMH36dEE1bY8TJ05gwYIFGDNmDA4ePIgxY8bgiSeewK+//gqA\nc0J9+eWX8eKLL2Lz5s3YsmULLly4AIBbSJYtW4YVK1b4fMLr1q07Ro4c5VZUCN82MY2lSu7YsRMA\n4Nq1ayJTiO+89MW7XE+dMBuK2K9Fq612u7w1H6LLmUL8Jx01YD+PBcuydscnf8yTqJCWKVhwphBe\nkKqsrAAAxMXFN0l7yHmTaC64JVjEx8fj+++/tzn+3XffoV27dm4/bMiQIVi4cCFGjhxpM4GxLIu3\n334bs2bNwogRI5CcnIwXXngBWq0Whw4dcnjP3bt3o1+/fpg7dy6SkpIwd+5c3HPPPdi9ezcA4PLl\ny0hJSUFmZiYyMzORkpKCy5cvC9cmJydjwIABbr+DJ7jjxGUvCyTA+SAwDONzG367dglQKpW4du0q\nDAY9FAqFT53PxLvgptrtiyfkqiouIsSVfwWPUqlCXZ3e71Io24sKMZvNdr9r/lxXu19X4aZKpcpv\nQkndwdr0U15eDrU6oMmEJ/vhpv4xHomWhVvi7IwZM7BmzRqcPXsWGRkZkMlk+Pnnn3Hw4EEsX77c\nKw0pKChAUVERsrKyhGMBAQHo27cvTpw4gQkTJti97uTJk5gyZYrk2MCBA7Fnzx4AQEpKCq5evYob\nN26AZVlcvXoVycnJKCgowDvvvIN//etfXmm/t7BXwwHwbdZN6fO5LIFXrlxGbW2Nz23i4oWmqTQW\n4t27VqsF4DoihEet5iJp/E31LC5Zz8OyZgcaCwaAwaW2jY+MsRcVUlNT61MzXlNgz4QWExPbLNrj\nb+ORaFm4NeomTJiAyMhI7Nq1S/BfSExMxJYtW3Dfffd5pSFFRUUAYGObjIyMRGFhocPriouLba6J\niooS7peUlIQFCxZg+vTpAICFCxciKSkJf//737FgwQL8/PPP2Lp1K1iWxZNPPunW+0RHu7foNITq\n6nCEhgYiLCxAeA7LslCrZYiKivDps3nuvjsNJSU3AXALrCfPdHVtSUkoQkM5gSkmJrxR3s8almUR\nGhqIkBA1FAoTQkMD0alTHMLCXLclJqYNzOY6BATIERkZipiYhjnsNcV7R0SEQKNRC88OCQmASiWz\naUtERDBqaxUu302pNN0Zu4GSe5jNZgQGMoiN9c74bYq+skdkZAiqqwMREaFBdXX1nXET36Tta9Mm\nGMHBKhiNRoSGBiI+PqLRwl39leYynloSLgULo9GI77//HnfffTfuv/9+nzfIGz8ClmUl95k4cSIm\nTpwo/M2Xeh8wYABGjBiB999/H2azGRMnTsThw4cRGRnp9P5FRVUet9ER5eU1qKysQVFRBUJCuOfU\n1NSgokKH4GDWp8+2oIRMpkJFRQXkcnWDnxkdHeLy2ooK7n0BQKs1NNL72VJdXQeGqURZmRaVlTWo\nqWGh17tui1ZrRGVlDbRaPZRKVYPa704/+YLqaj1qa03Cs8vKtDCZTDZt0Wr1qK11/d1UVlajsrIG\nJSVVknO1Wq5Pw8LMHr9nU/WVPSora1FZWYNbt8pRWHgLlZU1MJuVTdo+rdYAo7ESkZGh0Gr1KC52\n7J9GNK/x1NypjwDm0sdCoVBg3rx5gorYV0RHRwOwaC54SkpKnHpYR0VFCcWL3LmmrKwMW7duxapV\nq3Dy5El07NgRSUlJ6Nq1Kzp27Cg4fTYVYns/T2NEhFjTsWNnAL4Pn5T6WDRdDgiGUcBsNqG6uhoa\nTZDbvgBqNddmk8nkNxEhPAzDSMaZdRp5np4909CrV7rL+1kSZEmjQlqiS0KCzAAAIABJREFU4yYg\nTQhWUcE5boaFhTVlk+4ktjPdSXLnX+ORaDm45bx51113IS8vz6cNSUhIQHR0NI4ePSocq6urQ05O\nDjIyMhxel56eLrkGAI4ePerwmg0bNmDq1KlISEgAy7IS5zWDweCyWqGvsZd5symSC/GFkzQajU+f\n0xx8LPh21NbWoba2xq1QUx4+lwXgf45yfMl6Hi4qxFZj2LZtHNq37+DyfnzyN+vfkCXrZstJjgVI\nfRrKy8shl8sbPXeFNQoFI4Sbkn8F0VS4NfLmzZuHDRs24PHHH0ePHj1sssmFh4e79TCtVisIKGaz\nGTdu3MC5c+cQFhaG+Ph4TJs2Ddu2bUNiYiI6deqE119/HRqNBn/84x+Fe/ztb39DWloaFi1aBACY\nNm0apkyZgu3bt+O+++7DV199hZ9++gnvvvuuzfOPHj2KS5cuYd26dQCA1NRUXLlyBUeOHIHZbMaV\nK1eQmprq1rv4CnHpY57GyLppjVqtxvDhD/g8ykEsWDTljl+hYISw5voIFrzGAvCfiBAeLg+DdVRI\nwxcjS1SItcai8cdvY2DJG2FCZWUFQkJCmiQPixiuWjAnWFCoKdFUuDXyZs+eDYATMMS+C7wvw7lz\n59x62G+//YZp06YJf2dnZyM7Oxvjxo3Dhg0bMHPmTNTV1WH16tWoqKhAr169sGvXLslEn5+fj7i4\nOOHv3r17C/kpsrOz0b59e7z00kvo1auX5Nm1tbVYtWoVXnrpJWExi42NxapVq7BixQqwLIvVq1cj\nNrbpvLoB+/kFmiodsq+1FUDz0ljwuKpqKkbcZn/TWHCZI83C79hRVIi7OAo3ra3lCou1pKybgGXM\nVFZWwGQyITS0ac0gAGcKMZvNMBqNUCqdJ+MjCF/hlmCxe/durzhV9uvXT0hOZQ+ZTIb58+dj/vz5\nDs85cuSIzbGRI0di5MiRTp8dEBCAw4cP2xwfN24cxo0b5/TaxsS6IBbQND4WjUVz8bEQt6N+GgvL\n5O1vO0SxKp9fkFzVsnEGP0dYh5u21PHLC1JlZaUAgPDwNk3ZHADWgrp/CbpEy8GtmbBfv36+bgdx\nB0vioqbXWDQG4h1yU+74xfbo+vlY+K8phBdixYKFJxoLR7VC6upatsaCFyyag8ZC7Gztbxo0ouXg\ndBapqanBqlWrMGjQIGRmZmLRokUoLS1trLa1SvgFTmwKqa6uglKp9LuFyx14nxKgaX0s+EVCJpO5\nnXUT8HdTiDQZm3WYdn2xaCykPhaNlTW2seGFsMrKSgBNHxECSH9P4n8TRGPiVLB4+eWXsX//ftx7\n770YPXo0vv/+e6xcubKRmtY6sU61rNPpUF1djcjIxi9q1BiId8hN6WPBm0KCgoLqtbhKTSH+JViI\nU0Dbq2xaXxz7WDRO1tjGRmx2aMpU3mLEmjd/G49Ey8GpKeTLL7/E2rVrMXr0aADAn/70J0ycOBEm\nk6lF5fxvTsjlckmq5cLC2wDQpKmCfUlz8bHgd3f1cdwEuMmbc3xk/S68T+xjwWsZPI1qkMlkEsGC\nZVnU1dWiTZsIj+7bHBHPgc1BWwFITSG+zkFDEI5wOovcunULd999t/B3WloaGIZxmmKb8ByGsYQB\n8n0dExPTlE3yGeICV00Zqse3oz7+FTx8Lgt/2yGKwyW9obHgrxcLFnV1dWBZtkVqLMR9FRbmXsi9\nryHnTaI54HQWMZlMNoOTy9ZndHAF4Q24WHRuF1lUVIiAgMBm4RjmC/iJsCnNIOJ21FdjAVhyWfif\nj4W0iBYAj6JCAG6xFUeFWJJjtbzQx+aosRBrzfxNg0a0HJyOPJZlsXjxYolwodfrsXz5cok9cdu2\nbb5rYSuET7VcWVmBurpat7Ie+iv85NzU6bB5rUNDBDheKPK3cFOxo7BFsPAsrFwmk0ucN1t2RFPz\nEyzEwg4JFkRT4XTk2cvv8Kc//clnjSE4FAoGer1eMIPExrZt4hb5DrlcDpVKXa9IDF+QmJiEkJAQ\np3VpHME7cPqb6lkcFWIxhXgmWFibQvissWIn15YC33/NIZU3DzlvEs0Bp4LF+vXrG6sdhAg+1TLv\nuBkd3TL9K3iGD7+/yXdXKpUK7dolNOjamJhY6HRaaDRBXm6Vb7H4WBgF84V3fCwsGgs+h4V1GYCW\nAK8daA6pvHmkphASLIimgXRlzRA+WVFxcRFCQ0Nb5KQsxt/fLzExCYmJSU3djHojNoV4KypELpfZ\nrczbHEIxvQ1vAmtOES/SBFkUuUc0DSRYNEPETnUtNcyUaHos48zstagQ63DTllonBOBq6QwYMLBZ\npPLmkfpYkMaCaBpIsGiGiHcdJFgQvkJcl8ZbzpvWUSG1tTWQyWQtUmMBcCXlmxPSzJs0vRNNQ/Mw\nDBIS+MlBJpMhKiq6iVtDtFSk4aacKcTTcFOZzDqPRS1UKrVXihgSriHnTaI5QIJFM4Sf8CMiImnX\nQfgMS1SI0Ys+FpZw04qKcmi1Wr/3ofEneC2UTCaj7MhEk0GCRTOEnxDIDEL4EnsJsryVedNgMODY\nsR/Bsiy6devucVsJ9+A3IqStIJoSEiyaIcHBXPhafHx8UzeFaMGIy6bzfhGeJ8jirj9x4hdUVVWh\na9dkxMXROG4seMGCNJ1EU0KjrxnSqVNnxMe3a5FJhYjmg72oEE/V57zGo6AgD23aRKBHj1TPGknU\nC5lMBrlcThoLokkhwaIZIpPJSKggfI69suneiAoBuBwP99zTv9kkjmpNdOrUGQkJLTupHtG8IcGC\nIFop/KIvLZvumWDB75T79LkbQUH+lYm0pZCe3hvR0SEoKqpq6qYQrRQSLAiilcJHDkjzWHimYejZ\nMw2dOiU2qOYKQRAtAxIsCKIVI5czXq1uGhAQ0GKTYREE4R5kACWIVgzDMF5N6U0QBEGzCEG0YhQK\nRhJuSoIFQRCeQrMIQbRiOI2FEXd8N0mwIAjCY2gWIYhWjFzOeDXzJkEQBM0iBNGKUSgUMJvNMJlM\nADyPCiEIgqBZhCBaMXymTaPRAMDzqBCCIAgSLAiiFSOXc4KFwWC48zdNCQRBeAbNIgTRiuFLpxsM\nRgCeZ94kCIIgwYIgWjF8vRDeFEIaC4IgPIVmEYJoxfA+FmQKIQjCW9AsQhCtGIbhNBYGgx4AOW8S\nBOE5JFgQRCvGorHgfCwo3JQgCE+hWYQgWjHW4aZkCiEIwlNoFiGIVoxFsOCjQmhKIAjCM2gWIYhW\nDC9Y8JCPBUEQnkKCBUG0YqwFC9JYEAThKTSLEEQrhgQLgiC8Dc0iBNGK4cNNeUiwIAjCU2gWIYhW\nDPlYEAThbUiwIIhWjEJhESxIW0EQhDegmYQgWjFijQUJFgRBeAOaSQiiFcOXTQco6yZBEN6BZhKC\naMWQxoIgCG9DMwlBtGL4sukAOW4SBOEdSLAgiFYMaSwIgvA2NJMQRCuHFy7kctJYEAThOSRYEEQr\nh3fgJI0FQRDegGYSgmjl8H4W5GNBEIQ3IMGCIFo5DMNNAxRuShCEN6CZhCBaORYfC5oOCILwHJpJ\nCKKVwxciI8GCIAhvQDMJQbRySGNBEIQ3oZmEIFo55LxJEIQ3IcGCIFo5FG5KEIQ3oZmEIFo5FBVC\nEIQ3oZmEIFo55GNBEIQ3oZmEIFo5vI8FpfQmCMIbkGBBEK0c8rEgCMKb0ExCEK0c3hRCUSEEQXgD\nEiwIopVjMYXQdEAQhOc0y5lkz549GDZsGFJTU/Hggw8iJyfH6fnHjh3Dgw8+iNTUVAwfPhx79+6V\nfP7xxx9jyJAhuOeee7B+/XrJZ7dv38awYcNQXFzs9fcgCH+AFyhIsCAIwhs0u5nks88+w7p16zBn\nzhwcOHAAGRkZmDlzJm7cuGH3/Pz8fMyaNQsZGRk4cOAAZs+ejTVr1uDw4cMAgNLSUixbtgxLlizB\nzp078fHHH+Prr78Wrl+1ahXmzp2LqKioRnk/gmhuWEwhzW46IAjCD2l2M8lbb72FcePG4eGHH0ZS\nUhKWL1+O6OhoGy0Ez3vvvYeYmBgsX74cSUlJePjhhzF27Fjs2rULAFBQUICQkBCMGjUKaWlp6Nev\nH3JzcwEAhw8fRlVVFR566KFGez+CaG5Q5k2CILxJsxIs9Ho9zpw5g6ysLMnxrKwsnDhxwu41J0+e\ntDl/4MCB+O2332AwGNCxY0fU1NTg7NmzKC8vx+nTp5GSkoKqqips3LgRq1evpgmVaNVQHguCILyJ\noqkbIKasrAwmk8nGLBEZGYmjR4/avaa4uBiZmZmSY1FRUTAajSgrK0NMTAxeeOEFLFmyBLW1tRg7\ndiwGDRqE5557DuPHj0dZWRkWLVqEmpoaTJs2DRMnTnTZzujokIa/ZCuD+so9mrKfQkKUKCzsiO7d\nkxAV1fy/LxpT7kH95B7UT96nWQkWPPY0CM60CtafsSwrOX7//ffj/vvvFz7PycnByZMnsWTJEowc\nORIvvPACunTpgj/96U/o3bs3UlJSnLavqKjK7XdpzURHh1BfuUFz6Ke0tHvAss1/bDeHvvIHqJ/c\ng/rJfeojgDUr3WebNm3AMAyKiookx0tKShw6V0ZFRdlEdJSUlEChUCA8PNzmfL1ej5UrV2L16tXI\nz8+HwWDAgAEDEBMTg3vuuQfHjh3z3gsRBEEQRCujWQkWKpUKPXr0sDF7HD16FBkZGXavSU9Pt3t+\nz549oVQqbc7ftm0b+vfvj/T0dLAsC5PJJHxmMBgkfxMEQRAEUT+alWABANOnT8f+/fvx4YcfIjc3\nF2vWrEFhYSEmTJgAAHj66afx9NNPC+dPmDABt2/fxtq1a5Gbm4sPP/wQ+/fvx4wZM2zufenSJXzy\nySd48sknAQCdO3cGwzDYu3cvcnJy8OOPP6JPnz6N86IEQRAE0QJpdj4Wo0aNQllZGV5//XUUFhYi\nOTkZb7zxBtq1awcAuHnzpuT89u3b44033sD69euxd+9exMTEYOnSpRgxYoTkPJZlsXz5cjz77LMI\nDg4GAAQEBAiRIVVVVZgzZw5SU1Mb50UJgiAIogUiY3lPR8JtyNnHPcgxyj2on9yH+so9qJ/cg/rJ\nffzWeZMgCIIgCP+GBAuCIAiCILwGCRYEQRAEQXgNEiwIgiAIgvAaJFgQBEEQBOE1SLAgCIIgCMJr\nkGBBEARBEITXIMGCIAiCIAivQQmyCIIgCILwGqSxIAiCIAjCa5BgQRAEQRCE1yDBgiAIgiAIr0GC\nBUEQBEEQXoMEC4IgCIIgvAYJFgRBEARBeA0SLAiCIAiC8BokWAA4fvw45syZg0GDBiElJQUfffSR\n8JnBYMCmTZswZswYpKenY+DAgVi0aBFu3LghuYder8fzzz+Pfv36IT09HXPmzMGtW7ca+1V8irN+\nAgCWZZGdnY2BAwciLS0NU6dOxcWLFyXnVFRUYPHixejTpw/69OmDxYsXo7KysjFfo9ExmUzYsmUL\nhg0bhtTUVAwbNgwvvfQSjEajcI47fddaKCwsxJIlS9C/f3+kpqZi1KhROHbsmPA59ZUt27ZtQ0pK\nClavXi0co37i2L59O/7yl7+gd+/e6N+/P+bMmYPff/9dcg71lWP27NkjzF0PPvggcnJyXF5DggUA\nnU6H5ORkLF26FAEBAZLPamtrcfbsWcydOxcfffQRXnvtNdy8eROPPvqoZGFYu3YtDh8+jM2bN2PP\nnj3QarWYPXs2TCZTY7+Oz3DWTwCwY8cO7Nq1C8uXL8e+ffsQERGB6dOno7q6Wjhn0aJFOHv2LHbs\n2IGdO3fi7NmzePrppxvzNRqdHTt24N1338WyZcvw+eefY+nSpXj33Xexfft2yTmu+q41UFlZiYkT\nJ4JlWbzxxhv47LPPsHz5ckRGRgrnUF9JOXnyJD744AOkpKRIjlM/cRw7dgyTJk3Ce++9h927d4Nh\nGEyfPh3l5eXCOdRX9vnss8+wbt06zJkzBwcOHEBGRgZmzpxps7G2gSUkpKens//617+cnnPx4kU2\nOTmZPX/+PMuyLFtZWcn26NGDPXjwoHDOjRs32JSUFPbbb7/1aXubCut+MpvNbFZWFvvaa68Jx2pq\natj09HR27969LMuy7KVLl9jk5GQ2JydHOOf48eNscnIym5ub23iNb2RmzZrFPv3005JjTz/9NDtr\n1iyWZd3ru9bCiy++yP71r391+Dn1lZTKykp2+PDh7NGjR9kpU6awq1atYlmW+skZ1dXV7F133cX+\n5z//YVmW+soZDz30ELt06VLJsfvvv5/9xz/+4fQ60lg0AF6KDQsLAwD89ttvMBgMGDhwoHBOXFwc\nkpKScOLEiSZpY2NTUFCAoqIiZGVlCccCAgLQt29foQ9OnDgBjUaD3r17C+f06dMHGo2mRfdTnz59\n8NNPPyE3NxcAcOnSJfz4448YPHgwAPf6rrXw1VdfoVevXnjyySeRmZmJP//5z3jnnXfA3qk8QH0l\nZfny5RgxYgQyMzMlx6mfHKPVamE2mxEaGgqA+soRer0eZ86ckfQLAGRlZbnsF4UvG9YS0ev12LBh\nA4YOHYq2bdsCAIqLi8EwDNq0aSM5NzIyEsXFxU3RzEanqKgIABAVFSU5HhkZicLCQgBcP0VEREAm\nkwmfy2QyREREtOh+mjlzJrRaLUaPHg2GYWA0GjFnzhxMnjwZgHt911rIz8/Hu+++i0ceeQSzZs3C\nuXPnsGbNGgDAlClTqK9EfPDBB8jLy8PGjRttPqN+cszatWvRrVs3ZGRkAKC+ckRZWRlMJpPdfjl6\n9KjTa0mwqAdGoxGLFy9GVVUVXn/9dZfns62wvptYaHD3c5ZlXV7nz3z22Wc4cOAAXnzxRXTp0gXn\nzp3DunXrkJCQgPHjxwvnteQ+cBeWZdGzZ08sWrQIANC9e3dcu3YNe/bswZQpU4TzWntfXb58WfDn\nUqlUDs9r7f1kzfr16/Hzzz9j7969YBhG8hn1lX3s9YurviJTiJsYjUYsXLgQFy5cwD//+U+JdiIq\nKgomkwllZWWSa0pLS22kvZZKdHQ0AIv0z1NSUiL0QVRUFEpKSiQCF8uyKCsrkzjntTQ2btyIGTNm\nYPTo0UhJScHYsWPxyCOP4I033gDgXt+1FqKjo5GUlCQ5lpiYiJs3bwqfA9RXJ0+eRFlZGcaMGYPu\n3buje/fuOHbsGN599110794d4eHhAKifxKxbtw6ffvopdu/ejfbt2wvHaUzZp02bNmAYpkH9QoKF\nGxgMBixYsAAXLlzA22+/LQxEnp49e0KpVOL7778Xjt26dQu5ubmCuq2lk5CQgOjoaImKrK6uDjk5\nOUIfZGRkQKfTSexzJ06cgE6na9H9VFtba7M7YhgGZrMZgHt911ro3bs3rly5Ijl29epVxMfHA6C+\n4rnvvvvwySef4MCBA8J/PXv2xOjRo3HgwAF07tyZ+knEmjVrcOjQIezevdtGcKUxZR+VSoUePXrY\nmD2OHj3qsl+YlStXrvRh2/wCrVaL3NxcFBcX48MPP0RycjJCQkJgMBgQGBiIJ554AqdOnUJ2djaC\ng4Oh0+mg0+nAMAwUCgXUajVu376Nd955B3fddReqqqrw3HPPISQkBE899RTk8pYhvznrp9DQUBiN\nRmzfvh2dO3eGyWTChg0bUFRUhNWrV0OlUiEiIgK//vorDh06hO7du+PmzZtYsWKFEDfeUsnNzRUm\ne4VCgZ9++gmbN2/G6NGjMXDgQMhkMpd911qIi4vDq6++CrlcjpiYGPzwww/YsmULZs+ejbS0NOqr\nO6jVakRGRkr+O3ToEOLj4/Hggw9SP4lYtWoVDhw4gK1btyIuLk6YvwFu8aS+ckxwcDCys7MRHR2N\ngIAAvPbaa8jJycG6desE51d7yNjW6AhgxU8//YRp06bZHB83bhzmzZuH4cOH271u/fr1ePDBBwFw\nEu7GjRtx6NAh1NbWIjMzEytWrEBcXJxP296YOOunDRs2gGVZvPLKK3j//fdRUVGBXr164bnnnkNy\ncrJwbnl5OdasWYMjR44AAIYNG4bnnnvO6SD1d6qrq7F161Z89dVXKCkpQXR0NEaPHo3HHnsMarUa\nANzqu9bCN998g82bN+PKlSuIj4/H5MmTMXXqVMGuS31ln6lTp6Jr16547rnnAFA/8Vjn9+CZN28e\n5s+fD4D6yhl79uzBm2++icLCQiQnJ+PZZ59F3759nV5DggVBEARBEF6jZejoCYIgCIJoFpBgQRAE\nQRCE1yDBgiAIgiAIr0GCBUEQBEEQXoMEC4IgCIIgvAYJFgRBEARBeA0SLAiihXP69GmkpKSgoKCg\nqZviNaZOnYrVq1fX65phw4bhzTff9FGLLDzzzDOYPXu2z59DEM0VymNBEG5QWlqKl19+Gd9++y0K\nCwsRGhqKrl27YtasWTZlhZsbp0+fxkMPPYT//Oc/SEhIaOrmeIXy8nIoFAoEBwe7fU1paSkCAwMR\nGBjow5YBVVVVYFm2RSd9IwhnUHVTgnCD+fPno6amBmvXrkWHDh1QUlKC48ePo7y8vKmb1ugYjUYw\nDNOk1SD5Ilv1ISIiwgctsSUkJKRRnkMQzRUyhRCECyorK5GTk4OnnnoKmZmZaNeuHdLS0vD3v/8d\no0ePFs7T6/XYtGkTBg8ejPT0dPzlL3/Bf//7X8m9cnNzMWfOHPTp0wcZGRn461//igsXLgAAzGYz\nXn31VQwZMgQ9e/bEmDFj8NVXXwnXFhQUICUlBYcPH8b06dPRq1cvjBo1SlL8DgC+/fZbjBw5Eqmp\nqZg0aRKuXr0q+byqqgqLFy9GZmYmUlNTMXz4cPzzn/90+P7Z2dn44x//iI8++gj33XcfUlNTodPp\nwLIsduzYgfvuuw9paWkYM2YMDh48aNPeTz/9FFOmTEFaWhrGjh2L8+fP4/fff8eECROQnp6OiRMn\nIj8/X7guLy8Pc+fORVZWFtLT0zFu3Dh8/fXXkjZZm0KGDRuG1157Dc899xx69+6NwYMHY+fOnZJr\nrE0hKSkpeP/99/H4448jPT0dw4cPl7QfAH799VeMGzcOqampGDt2LP7v//4PKSkp+Omnnxz2l7Up\nZOrUqVi5ciU2b96Mfv36ITMzEy+88IJQhM4R+/btw7333otevXphzpw52LNnjyQ9tTv9NGzYMLzy\nyit45plnkJGRgSFDhuCzzz5DZWUlFixYgIyMDDzwwAP47rvvJNddunQJs2bNQkZGBjIzM7Fw4UKb\nKpcE4QgSLAjCBRqNBhqNBkeOHEFdXZ3D85599lkcP34cL774Ij755BOMGzcOc+fOxfnz5wEAt2/f\nxqRJkyCTyfDWW2/ho48+wqRJk4QF5u2338abb76Jp556Cp988gnuu+8+zJ8/H+fOnZM856WXXsLU\nqVNx8OBBpKamYuHChdBqtQCAmzdv4rHHHkNWVhYOHDiAKVOmYNOmTZLrt2zZgt9//x3bt2/H559/\njnXr1iE2NtZpHxQUFODQoUPYunUrDh48CLVajS1btmDfvn147rnn8Omnn2LWrFlYsWIFvvnmG8m1\nL7/8MmbOnIn9+/cLhfmef/55PPnkk/jwww9RV1eHtWvXCufrdDoMHjwYu3btwsGDB/HAAw9g/vz5\nyM3NddrG3bt3Izk5Gfv378fMmTOxadMmSSVde7z66quCQDFq1CgsXboU169fB8AV3Zs9ezYSExPx\n0UcfYfHixdi4caPT+znik08+AcMweO+997B8+XLs3r0bn332mcPzT5w4gWXLlmHSpEk4cOAAhg0b\nhuzsbMk57vbT22+/jdTUVOzfvx9/+MMfsGTJEixatAhDhgzBgQMHcPfdd2Px4sXC2C4sLMTkyZPR\ntWtX7Nu3D2+99RZ0Oh3mzp3rUhgiCAAASxCES/7973+zffv2ZXv27Mk+/PDD7IYNG9iTJ08Kn1+7\ndo1NSUlhr1+/Lrlu7ty57IoVK1iWZdnNmzez9957L1tXV2f3GQMHDmSzs7Mlx6ZMmcIuWrSIZVmW\nzc/PZ5OTk9m9e/cKn9+6dYtNTk5mjx8/zrIsy7744ovsAw88wJrNZuGcV199lU1OTmbz8/NZlmXZ\n2bNns88884zb7/7yyy+z3bt3Z4uKioRjWq2WTU1NFZ7Ls2bNGvbRRx912N4jR46wycnJ7OHDh4Vj\n//rXv9j09HSnbRg/fjz76quvCn9PmTKFXbVqlfD30KFD2QULFkiuuf/++yXXDB06lN25c6fwd3Jy\nMvuPf/xD+NtgMLBpaWnsgQMHWJZl2b1797J9+/Zla2pqhHM+/vhjNjk5mf3xxx8dtnXJkiXsrFmz\nJG19+OGHJec88sgj7P/8z/84vMeCBQvYGTNmSI4tW7aMTU5OdngNy9r2k3W/VFdXs8nJyezzzz8v\nHOO/p1OnTrEsy7Jbtmxhp02bJrlveXk5m5yczP76669On08QLMuy5GNBEG4wYsQI3HvvvcjJycGJ\nEyfw3XffYdeuXViwYAHmzJmDM2fOgGVZiWkE4Mwj/fv3BwCcPXsWvXv3tluGubq6GoWFhejTp4/k\neO/evfHtt99KjonV4TExMQA4x0SAM7X06tVL4v+QkZEhuX7ixIl44okncObMGWRlZWHo0KG45557\nnL5/bGwsoqKihL8vXbqEuro6PProo5JnGQwGtGvXzmF7IyMjAUBSNTIyMhI6nQ41NTUIDAyETqfD\nK6+8gm+++QZFRUUwGo2oq6tzWKXS3nMArm/4fnHnGoVCgYiICOGay5cvo2vXrggICBDO6dWrl9P7\n1adtJSUlDs+/fPkyhg4dKjmWlpaGDz74QPjb3X4S/x0UFITAwEBJ//PfK//eZ86cQU5Ojs24ATjz\nS1pamqvXJVo5JFgQhJuo1WpkZWUhKysL8+bNw9KlS/HKK69gxowZYFkWMpkM+/btg0Ih/VnxCxPb\nwAAsaydJ8f35z3gVtTvPGDJkCI4cOYJvv/0WP/74I2bPno2RI0di/fr1Dq/RaDSSv/nnvP7664iP\nj3fYPkftdfYOL7zwAv773/9iyZIl6NixIwIDA7FkyRIYDAan72WqFOW1AAAERElEQVT9XJlM5lJ1\n7+wa/jv1Bvae4+y7cufZ7vaTvWc763+z2YwhQ4ZgyZIlNs/kBUOCcAYJFgTRQLp06QKj0Qi9Xo9u\n3bqBZVkUFRUJGgprevTogY8//hh6vd5GaxEcHIyYmBj8/PPPyMzMFI7/8ssvSEpKqlebDh8+LFmY\nTp48aXNeREQExo4di7Fjx2Lw4MFYuHAhVq1aZVebYo+kpCSoVCrcuHFD0l5v8Msvv2Ds2LEYMWIE\nAKCurg55eXno1KmTV5/jiqSkJBw8eBC1tbWCcHjq1KlGe7b1s06fPi3521f91KNHD3z++eeIj4+H\nUqn06F5E64ScNwnCBWVlZZg2bRoOHjyI8+fPIz8/H59//jl27tyJzMxMBAcHo3PnzhgzZgyeffZZ\n/Pvf/0Z+fj5Onz6NN998E1988QUAYNKkSdDpdHjyySdx6tQpXLt2DYcOHRKcM//+979j165dOHTo\nEK5cuYKtW7ciJycHM2bMcLutEyZMwPXr17F27VpcvnwZ//73v/Hee+9Jztm6dSu++uorXL16Fbm5\nufjiiy/Qvn17t4UKgBOEZsyYgY0bN2Lfvn24du0azp07h7179+L99993+z726NSpE7788kucOXMG\nFy5ckDgWNiZjxoyBXC7HsmXLcOnSJRw9ehTbt28HYKtF8jZTp07F999/j507d+Lq1av48MMP8eWX\nX0rO8VU/TZo0CVVVVViwYAF+/fVX5Ofn4+jRo1i+fDmqq6s9vj/R8iGNBUG4ICgoCOnp6Xj77beR\nl5cHvV6P2NhY/PGPf8TcuXOF89avX49t27Zh06ZNuH37NsLCwpCamop+/foB4PwU3nnnHWzcuBF/\n+9vfAHD2bz5sctq0adBqtdi0aRNKSkrQuXNnZGdno1u3bm63NT4+Hq+88grWr1+P999/Hz169MCi\nRYuwePFi4RyVSoWXXnoJBQUFUKvV6NWrF7Zt21bvfnnyyScRFRWFXbt2YeXKlQgODka3bt3w6KOP\n1vteYp555hksXboUkydPRmhoKP72t781iWARFBSEbdu2YeXKlRg7diy6dOmCefPm4fHHH4darfbp\nszMyMvD8888jOzsbL7/8MgYMGICZM2diy5Ytwjm+6qfY2Fjs3bsXmzdvxqOPPoq6ujrExcVh4MCB\n9RI+idYLZd4kCIJwk6+++grz5s3D0aNHGy3hFs+6devwww8/4JNPPmnU5xJEfSGNBUEQhAP279+P\n9u3bo23btrh48SLWrVuHoUOHNopQsXPnTmRlZUGj0eDo0aN47733sHDhQp8/lyA8hQQLgiAIBxQX\nFyM7OxuFhYWIjo7GkCFD8NRTTzXKs3/77Tfs2rULVVVVSEhIwMKFCwUTGkE0Z8gUQhAEQRCE16Co\nEIIgCIIgvAYJFgRBEARBeA0SLAiCIAiC8BokWBAEQRAE4TVIsCAIgiAIwmuQYEEQBEEQhNf4/6wh\nTicaMCqSAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f00536b5cc0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"(df.groupby('seconds_left')\n",
" .foul_called\n",
" .mean()\n",
" .plot(c='k', alpha=PP_OBS_ALPHA,\n",
" label=\"Observed\", ax=ax));\n",
"ax.plot(pp_sec, pp_nba_trace['fc'].mean(axis=0),\n",
" label=\"Posterior expected\");\n",
"\n",
"ax.invert_xaxis();\n",
"ax.set_xlabel(NBA_XLABEL);\n",
"\n",
"ax.yaxis.set_major_formatter(pct_formatter);\n",
"ax.set_ylabel(NBA_YLABEL);\n",
"\n",
"ax.legend(loc=2);"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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nlVPbXX5jRMLC6XSFpJranR6e/zCbQ9Ui5ecDhWi1WkaMuACDwciePbubrClk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